Hmm, I guess my opinion is different from some others below.
My recommendations would be the National Archives, which has the original constitution, etc, which is at one end of the National Mall (it is one of the Smithsonian museums). The American History museum is close by, and it is also a favorite of mine. The other recommendation is a visit to the Lincoln, Korean, and Vietnam memorials, which are at the other end of the Mall and close together. I used to live in DC, and whenever I had visitors from out of town, these are the places that were first on my list to take them.
The other Smithsonian museums are great (Air and Space, Art, Natural History). And so is the zoo. But in my opinion, I can go to these types of museums/places in any big city. The Archives, American History Museum, and the monuments are unique to DC.