I was in DC for business last week, and stayed an extra day to check out the Smithsonian Air and Space museum annex at Dulles Airport in Virginia. It's about 30-40 minutes' drive from DC proper, and entry is free. There is a US$15.00 parking fee, however.
The museum itself is fantastic. It's like three large aircraft hangars brought into one building, and it's chock-full of amazing aircraft and space assets. Notable exhibits include the Space Shuttle Discovery, an SR-71 "Blackbird", the Enola Gay and an Air France Concorde. The museum has different sections for space flight, early aviation, WW2 aviation, the Cold War era and modern military. There's an IMAX theater there as well which is currently playing Star Wars Episode VII, but also shows some great movies about aviation, one of which being narrated by Harrison Ford.
I highly recommend visiting this museum if you're in the area. It's outstanding. The main Air & Space at the National Mall is very good, but this shows more experimental types.
Below is a picture of the Discovery in all its glory!