Smithsonian National Air and Space Museum - Udvar-Hazy hangar. Chantilly, Virginia

This enormous building isn't in Washington but is out near Dulles International Airport. It is by far and away the best collection of planes I have ever seen in one place. If you like aviation and flight, put this on your bucket list. It has the Space Shuttle Discovery, an SR71 Blackbird, and a full sized Concorde.

Note the heat shield tiles all over the shuttle 

The upper surface looks more like insulation than steel.