OK, well there's lots to see within range of the metro anyway, so that's fine. I guess you don't need me to tell you to see things like the stuff on the national mall and the Smithsonian and the like. There are of course quite a few interesting historical sites around the area. Old Town Alexandria has a church that was attended by George Washington, and later Robert E. Lee. The cemetery there includes the remains of Aaron Burr's (alleged) illegitimate daughter. You can also see black marks on some of the headstones, left from soldiers lighting campfires there during the Civil War. There's a tavern in Old Town that was frequented by several of the founding fathers, and you can also see the spot where some of the first shots of the Civil War were fired (depending on how you define the start of the war).
Within DC itself, there's Ford's Theater, if you want to see where Lincoln was shot (and the bed that he died in, which resides in a building across the street). You'll be visiting right when Spielberg's "Lincoln" movie comes out, so maybe they'll have some special event there?
I also kind of like the International Spy Museum, if you're into that sort of thing.
Oh, and keep in mind that DC is a very high crime city, so hopefully travel with people who know the area, so you know what neighborhoods to avoid. But in general, most areas directly around tourist sites should be OK, and most of the worst neighborhoods (as far as I can remember, as I haven't lived there in over 5 years) are east of the green line:
http://www.wmata.com/rail/maps/map.cfmand the area along the Anacostia River is especially bad. (Although I heard that might be changing, so my info might be out of date.)
