I'M BORED - What can I do now?" is the child's song of summer. Country kids can still find a brook to fish in, a tree to sit in or an open lot to play ball in. The city or suburban child finds that someone already owns the brook, the tree and the lot and has fenced him out.

What can an adult do with an itchy child on a hot, dull day? Here are several possibilities that can be done comfortably in a day's time.

All places are free unless otherwise noted. Hours and admission charges are open to change, and all refer to summer only.

Don't be afraid to create your own side trips, and if you find something really fascinating please write us about it.

FREDERICKSBURG, Virginia About 30 miles from Washington History buffs (young and old) will enjoy this town, which played a large part in both the Revolutionary War and the Civil War. Pick your era. It's advisable to take children from third grade up, who have had at least a smattering of American history.

Follow I-95 south to the Fredericksburg exit, where clearly marked signs will lead you to the VISITORS CENTER at 706 Caroline St. A 20-minute slide show will familiarize you with the history of the area, and the center will supply free parking passes and maps for the self-guided tour. If you walk or drive the tour, be advised that each building included has a separate admission charge. You can either buy a block ticket ($6 for those over 13, others free) or pay separately at each place. All buildings are open daily from 9 to 5.

Many of the tour stops are of only slight interest to children. One must, however, is STONER'S STORE, 1202 Prince Edward St. (adults $2, children up to eighth grade free). Guides in colonial costumes give a 40-minute tour of this restored general store, and children love the fascinating array of gadgets, many still in working order. There are butter churns, antique bicycles, sleighs, music boxes, ancient washing machines and hundreds of other items. Tours are tailored to the children's ages, and guides demonstrate machines and answer questions patiently.

Other places that might be of interest are the HUGH MERCER APOTHECARY SHOP, 1020 Caroline St. (adults $1, children 50 cents), which was operated from 1771 to 1776 and might attract youngsters of scientific bent; and the RISING SUN TAVERN, 1306 Caroline St. (adults $1, children 50 cents), built by George Washington's brother and a meeting place for early patriots.

If you arrive at Fredericksburg late in the day, or if your family would prefer to just get a brief overview of the town without entering each building, join the Junior Board's one-hour guided WALKING TOUR, which leaves from the Historic Fredericksburg Museum, 623 Caroline St., at 5 o'clock daily (through September 3, then Saturday and Sunday only through October 15; adults $2, six to 16 $1, under six free).

After you've seen downtown, head out to the National Park Service VISITORS CENTER at the Fredericksburg battlefield (9 to 5 daily). An electric map and dioramas help reconstruct the 1862 battle, a Confederate victory. Choose the guided walking tour or the self-guided driving tour, a pleasant ride through wooded hills.

If you wish to follow the Civil War's progress, head back toward town, go left on Littlepage Street, left again on William Street and out Route 3 west to CHANCELORSVILLE, the site of an upset triumph for Robert E. Lee. Then, if you're still not tired of the war, proceed four miles farther west on Route 3 to the WILDERNESS-SPOTTSYLVANIA area. Park Service guides in Confederate uniforms are available at various battlefield sites to answer questions and pose for pictures. All three sites are scenic and shady and all have picnic facilities.

If your family is interested only in its own battles, skip all the battlefields and stop at the new SHANNON AIR MUSEUM. From Fredericksburg ask directions to Route 17 and follow it south to Shannon Airport. Few people know about this small museum yet, so it's very casual. You can request special aviation movies or slides and curators will show them at your convenience. The museum houses a select collection of vintage airplanes, air paraphernalia and a replica of an early aeronautical machine shop. Watch current takeoffs and landings if you wish, or enjoy the airport restaurant. The museum is open daily from 9 to 5. Adults $1.50, children free.

LEESBURG, Virginia About 40 miles from Washington Leesburg and surrounding Loudoun County are reminders of genteel country living - a relaxing change of pace for citydwellers. This is horse country - rolling hills, open fields and farms. Leesburg's old houses have been preserved and, thankfully, there are no golden arches.

From the Beltway take Route 7 west. On the way you'll pass Colvin Run Mill, which is worth a short stop. Just before Leesburg, when the road forks, take the left fork. This will bring you in on Loudoun Street to the LOUDOUN MUSEUM AND VISITORS CENTER, where you can see a short slide show about the are's history and get information. (10 to 5 daily, 1 to 5 Sunday). Right next door is a restored log cabin, which may be open for viewing from time to time during the summer.

There's a pleasant walking tour of Lessburg, but most of the sights are not of interest to children. Drive the tour if you wish and return to Market Street (Route 7). Go west on Market Street to Morven Park Road and follow signs to MORVEN PARK, a magnificent 1,200-acre estate of mixed architectural styles. It was home to one Virginia governor and one Maryland governor. While parents tour the house children can play hide-and-seek in the boxwood gardens or explore the nature trails. The highlight for the children, however, is the Carriage Museum, where there are more than a hundred horse-drawn vehicles of all kinds, including sleighs, wagons and coaches - even an old hearse. (Open 10 to 5 Tuesday through Saturday, 1 to 5 Sunday.Adults $1.75, children 75 cents).

Plan the second part of your Leesburg trip according to your family's interests. There are two museums in people's homes that you can visit by appointment only, calling ahead from Washington or from the visitors center.

Families with DOLL-LOVERS should plan to visit Mr. and Mrs. Robert MacDowell in Aldie (703/777-6644).The MacDowells do ceramic, porcelain and glass restoration for the Smithsonian and the White House, and are experts at restoring antique dolls of all types. They have a basement full of exquisite dolls and doll houses, and are full of information about doll collecting.

Note: the MacDowells' valuable collection is not kept in glass cases, so they are quite concerned about damage. If you plan to go, you should explain to your children ahead of time that they must be careful and not touch the exhibits. If such restrictions might cause problems, do not take young children to the MacDowells.

To get to Aldie, go back into Leesburg and take Route 15 south. On the way you'll pass Oatlands, one of the properties administered by the National Trust for Historic Preservation (but not of interest to children) and the Mountain Gap School, a restored one-room schoolhouse (you might want to stop here briefly). After you cross Goose Creek, the MacDowells' home, "Oakwoods," is one mile farther south on the left. (Adults $1, children 50 cents)

Since this is hunt country, HORSE-LOVERS might want to meet Henry Buckardt, who runs the American Work Horse Museum in Paeonian Springs, four miles west of Leesburg (703/338-6290). He has blacksmith equipment, a collection of harnesses, oldtime tools and veterinary supplies and a fund of knowledge about work horses.

Take Route 7 west from Leesburg to Route 662. Make a sharp right onto 662 and Buckardt's place is the first one on the right. The horsey set might also investigate dates of horse shows, rodeos, polo matches and hunts in the area. Ask about these at the Leesburg Visitor's Center.

If your family likes country inns you may want to have lunch or dinner at the LAUREL BRIGADE INN on Market Street, where they are always ready to welcome kids. Or come home by way of WHITE'S FERRY, the last ferry still in operation on the Potomac. You may have a long wait because the ferry is small, but kids of all ages love the trip. The ferry runs from 6 a.m. to 11 p.m., weather permitting, and a one-way trip is $1.25 per car.

HAGERSTOWN, Maryland About 60 miles from Washington Downtown Hagerstown is an ugly tangle of one-way streets, but the City Park and sights in surrounding areas make it worth the trip. From the Beltway take I-270 west and then 70 west. Get off at exit 32 (U.S. 40) and go west into Hagerstown.

Families with young children might want to take a detour first. Instead of going west on 40, go east (away from Hagerstown) to the first left, which is Beaver Creek Road. Follow this for 2 1/2 miles and then turn left onto Beaver Creek Church Road to the old BEAVER CREEK SCHOOL. One classroom has been authentically restored so children can see just what it was like to go to school around 1900. The other room is a small museum. (OPen Sundays only, from 1:30 to 4:30, June 1 to October 1).

If it isn't Sunday, go fish. Again, follow U.S. 40 east, but take it until it intersects with I-66. Go left (north) on 66 one mile to the ALBERT M. POWELL STATE FISH HATCHERY. Learn how trout and salmon are raised from eggs to that stock Maryland's streams. (9 to 3:30 Monday through Saturday.)

p From either place you can take U.S. 40 west back into Hagerstown, where it becomes Franklin Street. Take Franklin to Prospect Street. Half a block down Washington Street is the MILLER HOUSE, headquarters of the Washington County Historical Society. The society ladies give tours of this elegant 19th-century home, which would bore most children. What may interest them, however, are two rooms full of antique dolls and toys, a collection of exotic clocks, the garden out back and the 1912 taxi in the stable. This is also the place to collect maps and ask questions. (Open 1 to 4 Tuesday through Friday, 2 to 5 weekends; adults 50 cents, no charge for school-age children.)

From here, continue out Prospect Street to the City Park area and visit the HAGERHOUSE, home of Hagerstown's founder (open 10 to 4 Tuesday through Saturday, 2 to 5 Sundays; 50 cents over 12, under 12 free).

Then drive up the road behind the art museum to the big yellow mansion that contains the VALLEY STORE MUSEUM, a recreation of the old-time country stores that stocked everything from clothes to coffins. (Open 10 to 5 Tuesday through Sunday, July 1 to September 1; adults 50 cents, children 25 cents.) Sit for a while on the store's spacious porch and enjoy the view of the park, or go down to the lake and feed the swans.All this adds up to a pleasant, relaxing day.

If you still have time, or if you have older children who are Civil War buffs, plan to go home by way of ANTIETAM NATIONAL BATTLEFIELD, 10 miles south of Hagerstown on Route 65. The visitors center (open 8:30 to 5) offers a short slide show and a driving tour of the battlefield sites (not as pleasant scenically as the drives through Fredericksburg and Chancellorsville, but possibly more interesting).

If you'd rather just enjoy dinner and a leisurely trip back, plan to return by way of Alternate U.S. 40. This is a lovely drive through old towns, past covered bridges and over South Mountain. Stop at WASHINGTON MONUMENT STATE PARK, which contains part of the Appalachian Trail plus many other inviting hiking trails. Even very young children can take the short walk up to the very first Washington monument (built in 1827) and enjoy the spectacular view of the valley below. There are several playgrounds in the park as well as picnic tables and outdoor fireplaces. If bringing your own dinner doesn't appeal, plan to eat at the OLD SOUTH MOUNTAIN INN, right across from the park entrance. All roads eventually lead back to I-70 and home.

THUNDERBIRD Archaeological Park and the Shenandoah Valley, Virginia.

About 80 miles from Washington Retrace the steps of prehistoric man at one of the most important archaeological sites in the Eastern United States. From the Beltway take I-66 south to its intersection with Route 55, then 55 west to Front Royal. From Front Royal take Route 340 south for six miles and then follow signs.

Mammoths and mastodons roamed the Shenandoah Valley some 12,000 years ago, when man first arrived. Nomadic groups began using the Thunderbird area as a base camp about 9,000 years ago because it was near a jasper quarry, a convenient place to fashion tools.

In 1971, when excavations were started by Catholic University, archaeologists found evidence of the earliest known structure in the New World. Twelve sites are currently being excavated and examined, although only one is now open to the public Archaeologists and student volunteers will be working at that site throughout the summer and will lead tours and answer questions.

At Thunderbird's museum, a short slide show and exhibits wild familiarize you with the area's geology and history, and the informative brochure will guide you down a relatively short nature trail to the dig. Where you can see how an archaeological site is excavated and maintained, what the diggers are looking for and how ancient man lived. Even young children can take this walk, but bring along a canteen of water if the day is hot - parents and older children tend to become fascinated, while little ones only get thirsty.Afterward you can enjoy a picnic lunch at tables near the museum.

The view across the Shenandoah River to the mountains is dazzling, and you can almost imagine how the valley looked thousands of years ago - but primitive man will soon be erased by suburbia. Several important sites are on the other side of the river, on property that developers have bought for vacation homes. Archaeologists will be able to continue their work, but the view may be spoiled, so visit the area soon. Thunderbird is open 10 to 5 daily. Admission is $1 for those over 60 or between 8 and 12; free for those under 8, and $1.50 for everyone else.

If you still have time or energy left after touring Thunderbird, explore LURAY CAVERNS (15 miles farther south on Route 340) or head back toward Washington and stop at SKYLINE CAVERNS (on Route 340 just below Front Royal).

City children might also be interested in the FAUQUIER LIVESTOCK EXCHANGE on Route 55 north of Marshall. Livestock auctions (cattle, sheep, hogs) are held every Tuesday from 1 to dark, and horse auctions (horses, ponies and tack) on the second Saturday of each month from 11 o'clock on. You can inspect the merchandise from walkways over the pens before the lively bidding begins.

If you have junior birdmen in your family, make sure to plan your Thunderbird trip for a Sunday and start early so you can arrive at the FLYING CIRCUS AERODROME in Bealeton by 2:30, which is showtime for wild airborne stunts like wing-walking (yes - someone walks on the wing of a plane while it circles and dips through the air), fancy formation flying, parachute stunts and other sky spectaculars. The Aerodrome also offers a small museum, light refreshments and a picnic area. Open Sundays only, from late May to October. Adults $3, under 12, $1. From Thunderbird take Routes 340 and 55 back to Marshall. Then go south on Route 17 about 20 miles to Bealeton.

GETTYSBURG, Pennsylvania About 80 miles from Washington Gettysburg again? Unlike some of the places listed here, Gettysburg is well known to everyone. Still, if you haven't been there in a couple of years there are new sights to see and your children may get more out of the trip than they did the last time.

From the beltway take I-270 north to Frederick, then Route 15 north toward Emmitsburg. In the Gettysburg area Business 15 will lead to the National Park Service VISITORS CENTER. Here an electric map pinpoints the action at the battle of Gettysburg; a slide show and other exhibits help you grasp the mood and setting of Lincoln's famous address. (Open 8 to 5 daily 8 to 5; electric map admission adults $1, children 11 to 14, 50 cents.) The Park Service also has information about walking tours of various lengths, bike tours, self-guided auto tours or a special guided auto tour ($8 per carload for two hours).

Before doing the tour you might want to stop at the CYCLORAMA adjacent to the visitors center for an in-the-round story of Pickett's Charge (8 to 5 daily, admission 50 cents for those 16 and over).

If you did all that the last time, try the National Gettysburg BATTLEFIELD TOWER, a four-year-old, 400-foot eyesore that now rises over the already shlocky, souvenir-ridden town. Children love to ride or climb to the tops of high places, and this one is worth the trip. You get a bird's-eye view of the whole battlefield area with continuous narration. This overall view makes the action much clearer in children's minds, so they might have more patience for the tour afterward. (Open 9 to 9 daily; admission $1.75 for adults, $1.25 for children six to 14.)

During your battlefield tour, plan to make a brief stop at GRANITE HILL FARM, which was worked by the Slyder family until the clash at Gettysburg turned it into a field hospital. Park Service interpreters have restored the farm and its blacksmith shop to pre-war condition, and you will find them reliving history; plowing, planting, cooking and washing in the fashion of the 1800s. (To get to the farm stop at the Big Round Top parking lot and follow the signs for a ten-minute walk. Open 9 to 5 daily.)

CALVERT COUNTY, Maryland About 40 miles from Washington There's a place for everyone. Fredericksburg and Thunderbird are more suited for older children, Calvert County ideal for younger ones. The trip is short and direct, many sights are on breezy Chesapeake Bay and none requires a long interest span.

From Beltway exit 34 take Route 4 south and east toward Prince Frederick. About 35 miles south of the Beltway, just past signs to Prince Frederick, look for Route 506 off to the right. Take 506 two miles to BATTLE CREEK CYPRESS SWAMP, the northernmost stand of cypress in the United States and an amphibian refuge. Only a bicentennial marker indicates the place, because the county is discouraging visitors until the area can be safely developed. Several trails should be opened by this fall, and a visitors center is planned for the near future. In the meantime you can admire the surrealistic, vine-covered trees and show your youngsters what a genuine swamp looks like, but don't explore . The area is hazardous, with ten feet of mud underfoot, snakes and blankets of poison ivy.

About ten miles farther south make another quick stop at the CALVERT CLIFFS VISITORS CENTER and nuclear power plant. The plant is off limits, but the visitors center features several exhibits about nuclear energy. Since the Calvert cliffs are a mecca for fossil hunters, the center also provides information about history, geology and fossil finds at the cliffs. View the plant and the bay from an attractive overlook. (Open 10 to 3 weekdays, 10 to 6 weekends.)

Two miles farther south of Route 2-4 is CALVERT CLIFFS STATE PARK, a pleasant lunch stop with picnic areas, pond, playground and trails to the cliffs. Most trails are two miles or more, a long hike for small children. Older children might find the walk worthwhile, however, because it's one of the view places in Calvet where you can explore the cliffs without trespassing. Since these cliffs are large hills of sand and clay that are slowly eroding from the bottom, the best place to find fossils is along the beach.

Because the winter and spring were very wet this year, be careful while exploring - wet eroding clay can create dangerous mudslides.

Most beaches are privately owned, so explore here or plan to pay for the privilege at one of the beaches open to the public. There are five public beaches on the Bay, some large, others small and fairly undeveloped: Chesapeake and North Beaches, out Route 260 just as you enter Clvert County; Breezy Point and Plum Point, east on 260 and south on 261; and Kenwood, on Route 509 at Port Republic. All charge admission.

If fossil-hunting looks too strenuous, head south again to Route 497 and the COVT POINT LIGHTHOUSE (open 9 to 4:30 daily excetp Monday). You can't climb the tower, but the Coast Guardsman on duty will tell you the light's history. You can also get a fine view of the cliffs, the bay and a new liquid gas dropoff station (from ships to pipeline).

Follow Route 2-4 to its end on Solomons Island. The town of Solomons is devoted to the sea and small children love to watch boats. Stop at the recently built CALVERT MARINE MUSEUM, a small, handsome collection of ship equipment and exhibits on the life of a waterman. On the grounds is the old DRUM POINT LIGHTHOUSE, which the children can climb up into. (Open 10 to 5 daily; 1 to 5 Sunday.)

End your day with a fresh seafood dinner on the pier and watch the sun set over the bay while the catch comes in. Little ones are sure to fall asleep as soon as they get into the car. Plan a leisurely drive home by way of the newly opened Lower Patuxent River Bridge into St. Mary's county. Follow Routes 235, 5, and 301 back to the Beltway.