If you're going to be in downtown DC, you want to stay downtown. Traffic and transit time makes going out of the city a pain. DC has some of the WORST traffic of any city in the U.S.
Air and Space is very cool, but check out some of the others on the Web. Natural History and American History are also good. The zoo is very good, but takes at least 1/2 day. It is easy to see the Lincoln Memorial, Washington Monument, White House and Capitol all in a single walk, plus other things (e.g., Vietnam Memorial). White House tours have to be booked in advance. The Spy Museum is also pretty good, but buy tickets in advance.
Nightlife areas in DC include Georgetown, Adams Morgan, and H St. in Northeast. The 9:30 Club is the best live music downtown, though there are a few other venues. The area around the Verizon Center near Chinatown also has tons of bars and restaurants, some of which are pretty good. I like Jaleo and Cafe Atlantico, personally. There are more college-type hangouts in the Foggy Bottom/GWU area up to Dupont Circle. The Brickskellar is well known for its wide selection of beers. The best pricey restaurant in DC is, IMNSHO, Citronelle in the Four Seasons Georgetown. Georgia Browns is also worth a look -- it is more casual and (slightly) less expensive, and serves southern American cuisine.