Virginians with horse sense will be at the Virginia Gold Cup at Great Meadows Saturday. The steeplechase action begins with pony races at noon; the serious racing starts at 1:30. The Cup, a tradition since 1922, drew a crowd of 32,000 last year, so you may want show up early to beat the traffic (tune in to 107.7 FM in Manassas for reports and live coverage) and stake out your area to tailgate. There'll be continuous entertainment until race time; gates open at 10. Tickets, $15 per car (up to 6 occupants), are available at Great Meadows in The Plains, which is 40 miles west of Washington off I-66 (take Exit 8 and follow signs). 703/347-2612. Breaking Away

The circumference of the Ellipse is exactly one kilometer. And on Sunday some of the world's best cyclists (500 entrants) turn that kilometer behind the White House into a race course at the 18th Annual National Capital Open. Participants include Olympic silver medalist Rebecca Twigg of Seattle and Californian Harvey Nitz, who also took a silver in Los Angeles and won this race last year. Junior-level races begin at 8:30 a.m.; the professionals begin rolling at 1. Spectating is free. 332-6986. Family Affairs

The nuclear family can go nautical in more ways than one this weekend.

*The Museum of Natural History hosts Sailing Ships and Old Salts, a free maritime program for families Saturday and Sunday from 12:30 to 5. You can listen to yarns being spun and chanteys being sung and see South Sea dancing (entertainment in Baird Auditorium) and demonstrations of such maritime arts and crafts as knot-tying in the Rotunda and Learning Center. The museum is at Constitution Avenue and 10th Street NW. 357-2700.

*There'll be a 12-man parachute team, the Navy's country and jazz bands, a firefighting demonstration and a fireworks display at the Naval Surface Weapons Center Open House. The free event is Saturday starting at noon in Silver Spring, a mile north of Beltway Exit 28-A on New Hampshire Avenue. 394-2865 or 394-2429.

*Sunday is Family Day at the Washington Navy Yard, where you can take tours of the Navy Museum, the destroyer U.S.S. Barry and the U.S.S. Fidelity, a mine sweeper up from Norfolk for the day. There'll also be horse and buggy rides, a Navy diving team, cannon demonstrations, music from four different Navy bands, crafts, children's games and ethnic foods. The free event is from noon to 6 at M and 9th streets SE. 433-2607 or 823-0630. Fest Break

Outdoor merriment abounds with spring festivals everywhere. Here are a few:

*Capitol Hill's Eastern Market is the site for the 24th Annual Friendship House Market Day, one of Washington's oldest street fairs. From 11 to 6 there'll be continuous entertainment, including Dixieland, Irish, folk and gospel music. Craftsmen show off their wares (there'll even be glassblowing demonstrations), and vendors offer varieties of American chili, and African, Mexican and Chinese food. The free festival is at 7th and Pennsylvania SE; 15,000 people turned out last year, so parking might be tight. By Metrorail, exit from the Eastern Market station on the Orange/Blue lines. 675-9050.

*The Bethesda-Chevy Chase Heritage Celebration kicks off Sunday at noon with a parade of jugglers, mini-cars, horse units, the U.S. Armed Forces Color Guard and others. It starts at Bethesda Elementary School, heads south on Arlington Road and east on Bethesda Avenue. Other free festivities this weekend in the downtown Bethesda area include a barbershop quartet concert, a kite rally and an antique automobile show. The celebration runs through May. For details, call 986-4190.

*You may want to check out the 59th Annual Shenandoah Apple Blossom Festival in Winchester (703/662-3863) or the 16th Annual Montpelier Spring Festival Sunday from noon to 6 at Montpelier Mansion in Laurel.(953-7882).

*Pick up a little soft shoe (and show) at Glen Echo Park's Dancefest '86, a two-day festival where you can learn about ballet and how to tap dance in open workshops. There'll also be performances around the park by 48 area dance companies. Festival hours are Saturday, 10 to 9:30; Sunday, 1 to 9:30. Admission is free, except to the shows at 5:30 and 8:15 each night in the Spanish Ballroom. Cost for those is $5; $4 for seniors and students. 229-6022. A Star is Bottled

What do Bob Hope, Pearl Bailey, Vincent Price, Kermit the Frog and Muhammad Ali have in common? They're just a few of the celebrities who've autographed bottles of wine to be auctioned at the Third Annual Celebrity Wine Auction at the Naval Hospital Officers' Club in Bethesda. Beginning at 1 Sunday, 42 East Coast and Canadian winery reps pour you samples of their wine. You can also munch on hors d'oeuvres until 4, when the auction starts. By Metrorail, exit from the Medical Center Station on the Red Line. Admission, $10, includes unlimited tasting. Proceeds benefit Homes for the Mentally Handicapped. 369-1300 or 926-0481. Rest of the Best IN TOWN

Browse through thousands of books, LPs and prints at the 37th Vassar Book Sale Friday and Saturday from 10 to 6; Sunday from 10 to 2, at 2445 M Street NW. 797-3638 . . . Guarneri Quartet cellist David Soyer gives a free performance of sonatas by Beethoven, Brahms and Prokofiev Friday at 7:30 at the Church of Our Lady of Perpetual Help, 1600 Morris Road SE. 699-5440 . . . The Inter-American Music Festival Concert Series begins this weekend with free classical music performances Friday and Saturday at 8 at the Organization of American States, 17th and Constitution NW. No tickets required. 946-8400 . . . Swedish violin virtuoso Nilla Pierrou performs with the National Chamber Orchestra Friday at 7:30 in the Kennedy Center's Terrace Theater. Tickets are $12. 857-0900 . . . Emily Dickinson: Letter to the World -- an extensive display of the poet's manuscripts, clothing and other items -- opens Sunday at 10 at the Folger Shakespeare Library, 201 East Capitol St. SE. Free. 544-7077. IN MARYLAND

The Cleveland Quartet and Meliora Quartet play the Mendelssohn Octet and, separately, quartets by Beethoven and Haydn Saturday at 8:30 in the Center of Adult Education, University of Maryland. Tickets are $10 and $12.50. 454-6534. IN VIRGINIA

There'll be folk music, dance and the work of more than 75 local artists 10 to 6 Saturday at the Herndon Fine Arts Exhibition held at Town Hall Square, Elden Street in Herndon. Free. 437-5484 . . . The Arlington Symphony plays a free concert of American music Sunday at 3 in Kenmore Auditorium, 200 S. Carlin Springs Road, Arlington. 739-2903.