EXPLORERS and stargazers in search of new worlds, cancel your other travel plans and take the Metro subway instead to the Foggy Bottom Station. Then walk six blocks south on 23rd Street to discover one of Washington's least-known National Historic Landmarks -- the 19th- century Naval Observatory, hidden in full view on one of the District's highest hills.

That gleaming silver dome that has long caught your eye as you passed on the freeway is now offering lively tours.

The main structure of the complex -- which has variously served as barracks, hospital, school and offices -- is the Federal-style brick building capped with the 23-foot dome. Although it's now the home of the Naval Medical Command, it looks much as it did in 1844 when what would become our national observatory was the Depot of Charts and Instruments, repairing and rating ship chronometers and maintaining charts. To provide navigation guidance, the depot gradually turned to astronomy to establish time standards that served the nation. And, by the end of the Civil War, it had become the observatory -- training astronomers and dispatching them around the world to observe eclipses and other phenomena.

Today you can still climb the worn wooden stairway that leads to the central rotunda where the first telescope rested on a two-story stone pier. You stand where the dome once opened to the sky, on the same spot where Abraham Lincoln stood long and silent one night during the Civil War.

In the south-wing rotunda -- which once housed the 26- inch great equatorial telescope, then among the largest in the world -- you're invited to stand where astronomer Asaph Hall discovered the faint objects that turned out to be the moons of Mars.

You can also see the observation shutters through which astronomers charted the stars. And, continuing to the east- wing residence of Matthew Fontaine Maury, the first superintendent, you climb red sandstone stairs to the parlor where Maury launched the science of oceanography.

Outside, gazing at spectacular views of the Potomac River below, you listen to the history of the hilltop site fringed with century-old oaks. Peter's Hill, University Square, Camp Hill, Observatory Hill -- the names hint at its story: By the 1790s the land belonged to a Georgetown merchant who deeded Peter's Hill to the government. The national university that President George Washington hoped for didn't materialize, so University Square became Camp Hill in the 1800s when the Marines who came with the new government from Philadelphia were housed there. In 1814, with the British on their way to burn the White House, citizen soldiers left Camp Hill to try to head them off.

When the War of 1812 ended, Camp Hill became an overgrown meadow, waiting almost 30 years before acquiring its next tenant and final name: Observatory Hill (the astronomical instruments were moved to new quarters on Massachusetts Avenue almost 90 years ago).

Don't let your touring end here, though. Foggy Bottom has more to offer at the base of Observatory Hill: the National Academy of Sciences and the State Department's diplomatic reception rooms.

Established in 1863, the National Academy of Sciences, like the observatory, was designed to foster scientific independence from Europe. Currently on exhibit are two shows: historical photos of the art and architecture of the academy; and tapestries designed by leading American artists.

After taking in the shows, continue your tour of the Academy in the remarkable Great Hall, a glory of green marble, cream stone and paneled walnut, lavished with murals, panels and medallions. Note the figures of earth, air, fire and water on the supports of the vaulted dome and the medallions depicting Egyptian subjects. In the library is a fireplace with carvigs outlining the history of writing, from the Spanish bison drawings in the Altamire Cave and Egyptian priests drawing hieroglyphics to the 16th-century Plantin press.

All the sculpture, inside and out, is the work of Lee Lawrie, best known for his Atlas sculpture in New York's Rockefeller Center. Note the doorway and the six large bronze window panels that depict major episodes and figures of science.

Riches of another sort await the explorer who ventures across the street from the Academy to the rooftop Department of State Diplomatic Reception Rooms, where you'll see what kings and queens entertained by the U.S. see: a showcase of American antiques and oil paintings that would be the envy of any museum, $30 million worth of Americana spread through nine rooms. The John Quincy Adams drawing room, considered one of the most beautiful rooms in North America, has the desk on which the final Treaty of Paris was signed and the desk where some believe Jefferson wrote the drafts of the Declaration of Independence. Among the treasury of riches: a $500,000 Chippendale desk made in Rhode Island in 1765 and a pair of matched Chippendale chests and oil paintings of Baltimore Harbor and Great Falls done in 1845 for King Louis Philippe of France. And providing a thread throughout the collection is the American eagle. Mahogany eagles are perched atop highboys, gold eagles are inlaid in chests, brass eagles are etched on drawer pulls and eagles painted on china and silver take wing.

End your tour on that soaring note, and you'll feel that you've had an adventure of the spirit as well. And not only is it in your own backyard, it's free. EXPLORNG A DIFFERENT HILL

NAVAL OBSERVATORY -- The next tours are December 28 at 2, December 31 at 10 and January 5 at 2, all free. There are also monthly week day tours. For reservations, call 653-1297.

NATIONAL ACADEMY OF SCIENCES -- Open 9 to 5 Monday to Friday. Refectory cafeteria generally open 11:30 a.m. to 1:30 p.m., Monday through Friday. For information about refectory 334-2222.

DEPARTMENT OF STATE -- Free tours of the Diplomatic Reception Rooms are conducted Monday through Friday at 9:30, 10:30 and 3. For reservations call 632-3241.