If You Have 1 Day
Make the Mall your destination, visiting whichever museums appeal to you the most. Then take a breather: If you have young kids, take them for a ride on the carousel across from the Smithsonian's Arts and Industries Building. With or without kids, stroll across the Mall to the National Gallery Sculpture Garden, where you can get a bite to eat in the cafe or relax by the reflecting pool. Rest up, dine in Dupont Circle, stroll Connecticut Avenue, then take a cab to visit the Lincoln Memorial at night.
If You Have 2 Days
On your first day, take a narrated tour of the city for an overview of the city's attractions, stopping at the Jefferson, FDR, Lincoln, and Vietnam War Veterans memorials, and at the Washington Monument. Use the tour to determine which Mall museums you'll want to visit. After taking in the Washington Monument, walk up 15th Street to F Street, turn right, and walk to Red Sage at 14th and F for some Southwestern fare in the restaurant's open-all-day Border Café (which doesn't take reservations). Following lunch, visit your top-pick museums on the Mall.
Start your second day by visiting the Capitol, followed by a tour of the Supreme Court. Walk down Pennsylvania Avenue to Seventh Street for lunch at Montmartre, then spend the afternoon visiting the Library of Congress, the Folger Shakespeare Library, and, if you have time, Union Station and the National Postal Museum. Have dinner in Georgetown and browse the shops.
If You Have 3 Days
Spend your first 2 days as described above.
On the morning of your third day, tour the International Spy Museum, followed by the City Museum. Enjoy a late lunch downtown near the MCI Center, such as at Poste, Zola, or Bistrot D'OC, and then visit the National Museum of Women in the Arts. Have a pretheater dinner at one of the many restaurants that offer these good deals (1789 in Georgetown and the Bombay Club near the White House are two fine choices). Then head to the Kennedy Center for a performance.
If You Have 4 Days or More
Spend your first 3 days as suggested above.
On the fourth day, visit the U.S. Holocaust Memorial Museum (not recommended for children under 12); this will require most of your day. Have dinner in Adams-Morgan, followed by club-hopping up and down 18th Street. (Or take in a salsa lesson at Habana Village, on Columbia Road in Adams Morgan.)
If you have a fifth day, consider a day trip to Alexandria, Virginia. Or board a boat for Mount Vernon and spend most of the morning touring the estate, with the afternoon set aside for seeing sights you've missed. Have dinner in downtown Washington at one of the Seventh Street-district restaurants, then see Shakespeare performed at the Shakespeare Theatre, or head to the Blue Bar at the Henley Park Hotel to sip a nightcap as you listen to live jazz.