The state capital of Maryland, Annapolis has been privy to much of the important political decision-making in the state. As the site of the U.S. Naval Academy, Annapolis is a vital cog in the military machinery of our nation. And the city is situated on the shore of the Severn River near the entrance to the Chesapeake Bay, thus providing economic and recreational advantages to both residents and tourists. TIMING

Weather should be a major consideration for any visit to the city. A dreary dock area in ran and fog, the historic histrict is lively and thriving under warm, balmy conditions. This is the perfect time of year to begin enjoying boating, fishing and strolling. The state legislature is no longer in session, however, so count poltician-watching off your list of things to do; politicians are out of season. THE FESTIVAL WEEKEND

The Annapolis Fine Arts Festival is this weekend, June 16, 17 and 18. The three-past festival at the city dock encompasses the performing arts, arts and crafts for exhibit and sale, and a discovery tent for children ages 3 to 12 with a "Wizard of Oz" theme. Admission, $2.50 for adults and $1 for children, can be bought at the gate. The festival will run 11 to 11 on Friday and Saturday, 11 to 8 on Sunday. Beer, hot dog, burgers, corn dogs and french fries will be available on the grounds. If you prefer, get your hand stamped so you can leave, get something to eat and get back in without paying twice. All-day parking will be set up at the Navy-Marine Corps Stadium on Rowe Boulevard; cost is $1, with free shuttle-bus service to the dock.

Friday and Saturday there'll be entertainment for children (magicians, puppets, mime and gymnastics) until 6, with the evenings given over to adult entertainment: "An Evening of Folk Roots" Friday and "An Evening of Potpourri," including an African dance group and the Peabody Ragtime Band, Saturday. Sunday features an all-day bluegrass mini-festival, with numerous bands and three groups of cloggers. For more information, call 301/267-7922. TRANSPORTATION

Take U.S. 50 (June Hanson Highway) east from the Capital Beltway, then follow signs to Annapolis, Naval Academy. The drive takes approximately 30 minutes. Free visitors' parking is provided at the Academy. There is metered parking around the dock and Market Square, but on warm, sunny weekends the tourists arrive in full force, so expect to search a bit. You'll want to walk once you're in the city, for that's the only way to soak up the historical lore and congenial atmosphere.

Greyhound Bus Line is another option; the bus leaves you off at 127 Main St. HISTORY

Named for Princess Anne in May 1695, Annapolis was a thriving colonial seaport with sugar, molasses, rum and tobacco shipped through the docks. Since the city was the first peacetime capital of the United States, George Washington resigned his commission as Commander-in-Chief of the Continental Army on December 23, 1783, in the Maryland State House. Then on January 14, 1784, the Continental Congress ratified the Treaty of paris ending the Revolutionary War. THINGS TO DO AND SEE

There are several places to see in the historic district, including the Maryland State House, Old Treasury Building, U.S. Naval Academy, Annapolis waterfront and St. John's College. Architecture buffs will want to see several of the 18th-century mansions as well: William Paca House (c. 1765), Hammond-Harwood House (1774), Chase-Lloyd House (1769-74). You can see it all yourself or take one of several walking tours available through Historic Annapolis Tours, Inc., Old Treasury Building, State Circle, Annapolis 21401. 301/267-8149. June through August they have regularly scheduled tours on weekends at 10, 1:30 and 3. You might also try Three Centuries Tours, P.O. Box 29, Annapolis 21404. 301/263-5357.

The best way to see the harbor is on the double-decker sightseeing boat, The Harbor Queen, which leaves the city dock every hour on weekends from noon to 6. This 40-minute narrated cruise is well worth the fare ($2.20 for adults, $1.00 for children under 12). The same company also offers a seven-hour cruise on the bay to St. Michaels on the Annapolitan II. This cruise takes two hours each way, with three hours in between for enjoying lunch on St. Michaels and visiting the Chesapeake Bay Maritime Museum. Reservations should be made through Chesapeake Marine Tours, Inc., P.O. Box 3323, Annapolis 21403. 301/268-7600. MIDSHIPMEN'S HAVEN

Established in 1845, the United States Naval Academy is a major element in Annapolis' attractiveness. Stop at Ricketts Hall just long enough to pick up a brochure with accompanying map. The campus is relatively easy to maneuver around, and a do-it-yourself approach is more relaxing. But from 10 to 3, guided tours are available - $1 for adults, 50 cents for children under 12. 301/263-6933.

Definitely visit the chapel, where Sunday services are open to the public and where the crypt of John Paul Jones is located. Then visit with Tecumseh, a bronze replica of the figurehead off the USS Delaware.During exams, midshipmen toss pennies at the statue for good luck and pay their respects with left-handed salutes. The Brigade of Midshipmen forms in Tecumseh Court at 12:10 Saturday and 12:30 Sunday; the ceremony includes formation and a performance by the Drum and Bugle Corps, but June week has passed and the midshipmen are at sea with the fleet for the summer. Formation won't begin again until after the new plebes arrive for summer training on July 6. Meantime, you can play admiral by inspecting a sample midshipman's room open to the public in Bancroft Hall, residence of all 4,300 midshipmen and women. SHOPPING

Down by the waterfront, the recently opened A.L. Goodies Mini-Mall at 36 Market Space contains several shops with an assortment of "goodies": Big Dipper for ice cream, Fudge Kitchen for candy made before your eyes on large marble slabs, Kites Aweigh for flying toys ranging from $2.25 to $305, This End Up Furniture Co. for crate chairs, and more. Then around the corner at 112 Main St. is another group of stores - More Goodies Mall - with additional merchandise: various headgear at Hats in the Belfry, silk-screened fabrics at Marblehead Handprints, and several boutiques - all with pervasively enticing smells enanating from the Gingerbread Man bakery.

More shopping and antiques can be found along Maryland Avenue. But if yo prefer to stay by the water, visit Dockside Tintype Studio at 118 Dock St. There you can don a Civil War uniform and have your picture taken in an imitation process of the old-time tintype, popular from its inception in the 1980s until George Eastman introduced a flexible film around 1890. FOOD

Close as it is to the Chesapeake Bay and Atlantic Ocean, Annapolis has always been a great spot for seafood. The enclosed Market House offers a wide variety of food - raw oyster bar, ice cream, bakery, fried chicken - if you want to stand and munch with the other tourists. A gastronomic delight is the weekend seafood buffet upstairs at Fiddler's Green, 136 Dock St; $6.95 gets you all the steamed shrimp, crab cakes, casseroles, fish salads and fruit you can eat. Another excellent spot to quell hunger pangs is McGarvey's Saloon at 8 Market Space, with excellent burgers and fries, huge omelettes and a friendly atmosphere. Don't confuse it for Riordon's Saloon, just down the street at 24 Market Space. By contrast, Riordon's has terrible service, an overbearing atmosphere and the food is not worth the trouble. Stick to McGarvey's. Other restaurants worth trying include Harbour House on the city dock for seafood and steaks; Middleton Tavern at 2 Market Space for history (the building dates to around 1750), Caesar salad and stuffed sole; Dockside at 22 Market Space for seafood and steaks; and Auberge de France at 186 Main St. for French cuisine (closed Sunday). ENTERTAINMENT

Annapolis Summer Garden Theater is an outdoor theater with a three-quarter stage and seating for 150 people. The reason schedule includes "Mame," now through July 9, and "Once Upon A Mattress," July 21 through Sept. 3. Performances are Thursday through Sunday evenings, curtain at 8:45. Tickets ($4.75) can be bought in advance or the day of the play.

Colonial Players of Annapolis is presenting a British comedy, "The Knack," July 7 through 29. Friday and Saturday performances cost $4.00, curtain is at 8:30. Sunday shows are $3.50, with a 7:30 curtain. 108 East St. 301/268-7373.

A diversity of live music is available in town as well. King of France Tavern in the Maryland Inn at Church Circle features jazz. Th upcoming schedule at this popular club includes Dick Hyman June 16 to 18, Charlie Byrd Trio June 20 through July 16, Earl "Fatha" Hines July 18 through 23 and Ethel Ennis July 25 through Aug. 6. Showtimes are 8:30 and 11 Friday and Saturday, 8 o'clock Sunday. Cover charge is $4.00. 261-2206.

Fiddler's Green at 136 Dock st. is named for the undersea paradise in nautical folklore where good sailors or those who die peacefully ashore go. So it shouldn't be a surprise that the entertainment tends to Irish and traditional British seafaring tunes sung by John Longbottom (June 16 and 17, then again for the 4th of July weekend, June 30 through July 3) and sing-alongs of traditional American songs (June 23 and 24 with Stuart Horsman on autoharp, guitar and dulcimer). 301/263-8844.

Other Annapolis music spots include Fran O'Brien's at 113 Main St.(301/268-6288) for top-40 songs and dancing; The Library, 1803 West St. (301/261-2877) for a book-lined atmosphere along with the music and dancing; Charlie's West Side at 25 Annapolis St. (301/263-8396) for bluegrass every night but Sunday; and the Annapolis Hilton's Skippers Pub (301/261-2240) for a piano player Tuesday through Saturday nights, or a guitarist at the dock bar Sundat from 2 to 6.