BUILDING A CITY in the middle of a swamp isn't such a bad idea. For one thing, it gives people a good excuse to clear out of town during August. But even better than that, it guarantees terrific views of the city from the surrounding hills.

Washington, swamp that it was, abounds with lovely vistas. So lovely in fact that bets are off on finding the "best view of Washington." When seven different people with noteworthy points of view were asked to name their favorite view of the city, they offered seven different answers. A few folks even had several favorite views.

Only one person refused to summon up a favorite. As regional director of the National Park Service, Robert Stanton probably had visions of ranger wars if he pitted the view from the top of the Washington Monument against the view from the steps of the Lincoln Memorial.

But when pressed, Stanton is willing to recommend a "fantastic" view which is sometimes overlooked: the view of the Capitol from Cedar Hill, Frederick Douglass's home in Anacostia. From the northwest corner of the restored home, the panorama of a sprawling Washington is hidden behind a stand of oak and sweet gum trees. Within the branches of these trees, though, is a natural window which frames a lovely view of the Capitol dome. From the rocking chairs on Douglass's front porch, visitors can also catch glimpses of the Anacostia River below, look over the top of RFK Stadium and see the Shrine of the Immaculate Conception looming in northeast Washington.

Across town on another hill, the Rev. Canon Charles Martin, the retired headmaster of St. Albans School, is quick to pinpoint his favorite vantage point, then just as quickly add two more views of note. The view from the foot of the Peace Cross on the grounds of Washington Cathedral has been a favorite of the headmaster for years. Even as buildings and trees have grown up around the expanse of lawn where the Peace Cross stands, Martin has enjoyed the view and its vistas of downtown, including the Capitol dome and the tower of the Old Post Office.

Martin also finds inspiration in the view of Mount St. Alban seen driving up Massachusetts or Wisconsin avenues, where "the cathedral rises from the confusion of the city. It's startling and very impressive to see the total cathedral, clear against the sky."

Finally, Martin points out that the western views from the cathedral's Observation Gallery overlook the whole of the Potomac Valley, past the rising concrete of Tysons Corner and to the distant Blue Ridge of Virginia. The other views from the gallery are equally impressive, whether looking towards the cathedral's towers, buttresses and gargoyles or looking off to the city, where the Potomac gently curves around Rosslyn and flows beyond the Jefferson Memorial.

Skip Hartman encourages his out-of-town visitors to take in a view of Washington from a Virginia hillside. Hartman is a board member of the D.C. Committee to Promote Washington, a nonprofit corporation that advertises the city's tourist attractions to other metropolitan areas. He is also the directing manager of Loew's L'Enfant Plaza Hotel and so is quick to note that his favorite view of Washington is from the 14th floor of his hotel, "particularly during the fireworks on the Fourth of July." But he admits that he also likes to steer people towards the gravesite of Pierre-Charles L'Enfant, who rests in front of the Custis-Lee mansion in Arlington National Cemetery.

L'Enfant, the first to design the layout of Washington, died a pauper in 1825; in 1909, he was reinterred with honors on the front hillside of Arlington House, the former home of Robert E. Lee. From the hill, visitors have sweeping views over the Potomac and across the dramatic Memorial Bridge to the center of the District. The flatlands of downtown in Northwest squat to the left, while all the major monuments and domes rise above the trees of the Mall and parkland. The District's distant grid of streets and traffic circles lies at the feet of the one who first envisioned them.

At the far end of L'Enfant's grand mall lies Jenkins Hill, which the French engineer referred to as "a pedestal awaiting a monument." It was here that L'Enfant placed the "Congress House" in his elaborate scheme, and where the Capitol building sits now. The base of this hill serves as the vantage point for the favorite view of Howard Nemerov, the poet laureate of the United States.

"I never go anywhere I can't walk," says the poet, who has an office in the Library of Congress. Nemerov enjoys walking on the Capitol grounds, but his favorite view is from "the great Civil War statuary of Ulysses S. Grant at the foot of the hill."

Grant sits high on his horse with his hat pulled low over his brow as he surveys the Capitol Reflecting Pool and the Mall stretching out below his perch. His statue is surrounded by four lions and flanked by two scenes of charging Civil War cavalry and infantry troops. Beyond the pool lies the Mall with its avenues of trees and wide gravel paths. The towers and flags of the Smithsonian Castle rise from the cluster of trees on the left, while the Washington Monument rises stiffly from the far reaches of the Mall.

Leaving pedestrians behind, Tom Whitford cruises the Potomac to find his favorite view of the city. The past commodore of the Capitol Yacht Club and present captain of a charter boat business, Whitford steers his friends and clients to a stretch of the Potomac, just upriver of Georgetown, where the city virtually disappears from view.

"People who have lived in Washington for 40 years have not seen Washington from that perspective," he says, "and it's only 15 minutes from the White House."

Whitford's charter boat, the Irish Mist, motors under the 14th Street Bridge and up past Georgetown until only forested banks and the boulder-strewn waters of the Potomac surround the boat.

"It's a pastoral setting, delightful, soporific," says captain Whitford.

When making the run, Whitford tries to time his turnaround at sunset, so that as the boat rounds the bend in the Potomac where the city magically reappears, the moon sits on the tip of the Washington Monument and the lights from Washington Harbour and the Kennedy Center sparkle on the river's surface.

From the air, there is only one choice -- "daytime or nighttime" -- for traffic pilot Walt Starling's favorite view: from Wheaton. Wheaton, Walt? Yep, from a plane high over the suburbia of Wheaton, the man-in-the-sky for radio station WLTT-FM says that viewers look over most of the city "back through Rock Creek Park, over the whole of Northwest and Northeast, from Catholic University to Connecticut and Wisconsin avenues, over to Anacostia Heights, all the way to Arlington Ridge."

While flying over Wheaton in a small plane might not be everyone's cup of tea, few would turn down sampling the views and drinks offered at D.C. City Administrator Carol Thompson's favorite viewing spot: the Sky Terrace on top of the Hotel Washington. Most summer evenings find lines of eager viewers waiting for a few of the green wicker chairs to be vacated so their viewing pleasures can commence.

Table-hopping is sanctioned as view-seekers work their way closer to the tables along the terrace's edge. With breezes rippling treetops and flags on federal roofs, customers can while away the evening watching the traffic chase itself or gazing at the white monuments bathed in light. As you pay for your round of drinks, you can impress your out-of-town visitors with the fact that the buildings pictured on the backs of the $5, $10, and $20 bills are all visible from the hotel's rooftop. As the views on the bills disappear from your hand, your eyes can drink in the real thing.

FREDERICK DOUGLASS NATIONAL HISTORIC SITE --

Cedar Hill, 1411 W St. SE. 426-5960. Open daily 9 to 5 through September; from October through April, 9 to 4. Last guided tour at 4:30 (3:30 during winter hours).

WASHINGTON CATHEDRAL --

Wisconsin Avenue at Woodley Road NW. 537-6200. Observation Gallery open Monday through Saturday 10 to 3:15, Sundays 12:30 to 3:45 (closing time on Sundays may vary according to the volume of visitors). The Peace Cross stands on the south side of the cathedral grounds, near St. Albans Church.

L'ENFANT'S GRAVE --

Arlington National Cemetery. 692-0931. Cemetery open daily 8 to 7; Robert E. Lee's Arlington House open daily 9:30 to 6.

POTOMAC CRUISES --

Only small or low boats can get under the 14th Street Bridge and head towards Georgetown. Charters include the Happy Daze VI (569-8708), the Admiral Tilp (684-0580), the Irish Mist (861-1991) and the Dandy Restaurant Cruise Ship (683-6076). The Dandy offers daily lunch and dinner cruises and makes its turnaround near Georgetown; prices range from $25 for a three-course weekday lunch cruise up to $55 for a five-course Saturday dinner and dancing cruise. The Irish Mist travels further up the river to the captain's special viewing point, where the city is no longer visible. The Irish Mist can be chartered for $500 for a three-hour cruise accommodating up to 26 people. People are free to bring their own food and drinks. Two-hour cruises for up to 50 people on the Admiral Tilp start at $500; the boat can go under the 14th Street Bridge only under certain tide conditions. The Happy Daze VI also travels to Georgetown when the tides are right. A three-hour cruise for up to 50 people, including open bar, costs $1,400.

AERIAL VIEWING --

Walt Starling suggests calling the area's small airports to find a charter operation that provide planes and pilots for air tours. Flights for two to four people run anywhere from $65 to $95 an hour. For more information, look under "Airports" in the Yellow Pages.

THE SKY TERRACE --

The Hotel Washington, 15th Street and Pennsylvania Avenue NW. 638-5900. Open daily 11:30 a.m. to 1:00 a.m. Lines form during evening hours, primarily from 5 to 8; but with the terrace seating capacity around 160, they usually move quickly.

Mary Ellen Koenig last wrote for Weekend about tramping through the woods in search of beaver lodges.