Well, it's over a decade since I was there, so things may have changed.
DC has to be a bit like London, there's plenty to do, you can't throw a brick without hitting something of interest, it just choosing what's the best use of your time.
I spent a short time at the Arlington Cemetery, which was interesting, although we did seem to confuse some USAians, since we walked there from the Mall, and I don't think saw another pedestrian in that short distance, the couple of cyclists we met didn't seem to be prepared for the sight of someone walking around there!
I guess it's also worth having a look at things like the reflecting pool, and the memorials around the Mall, as well as obviously having a peer at the Whitehouse. When we were there, we didn't even attempt to do the Washington Monument, since it was one of the hottest and most humid August's at the time, and the interior would have been horribly hot and unpleasant.