I have already written about the National Air and Space Museum’s surprisingly good country cousin in Kansas. The larger museum on the National Mall in Washington is an absolute must-see (and try to visit the annex at Dulles International Airport as well).

National Air and Space Museum entrance hall, with the Apollo 11 command module on the left (photo by Jawed Karim)
There is lots to see in the Washington museum – the Apollo 11 command module and the Wright brothers’ aircraft, for example – and lots to do. And the museum is free, although the IMAX theatre, planetarium, and flight simulators are not. For young children, there are story times. See also the floor plans and a list of aircraft on display at this superb museum.
If you can’t visit, there are online exhibits, a multimedia gallery, a blog, and images and video from the public observatory.
Note: the museum is currently closed due to the US federal government shutdown.