I second the METRO idea. Its very clean, fast & cheap. It'll get you into Maryland, DC & VA. After you see all the parks and museums, hop on the METRO and head into Maryland, get off at the Bethesda METRO stop and walk around a bit. There are tons of outdoor restaurants, coffee houses, bars as well as movie theaters in downtown Bethesda and its all within a five minute walk from the METRO station.
If you're staying @ American University, hop on the metro and head for the Chevy Chase METRO stop, there are two really nice malls there, I highly suggest going to the "Cheesecake Factory" for lunch or dinner; it's awesome.
Also, you'll be walking distance to the National Cathedral. Do yourself a favor and go in and walk around. Its very impressive! Go downstairs and look around in the lower floors, really cool stuff to look at.
You'll also be 5 minutes by cab to Georgetown, by all means go walk around. Lots of nice restaurants & bars.
If you're looking for more "adult" entertainment, you'll be about 5 minutes away from "GoodGuys"....right outside of Georgetown. But of you want the BEST, then take the METRO to "Faragut North" and walk to Camelot, a world class establishment.
>Have fun