Chantilly, VA
I have not been to the one in DC, but the Udvar-Hazy Air and Space Museum is quite cool!
From wikipedia The Concorde is a retired turbojet-powered supersonic passenger airliner or supersonic transport. Among other destinations, Concorde flew regular transatlantic flights from London Heathrow and Paris-Charles de Gaulle Airport to New York JFK and Washington Dulles; it flew these routes in less than half the time of other airliners. Concorde was retired in 2003.
I got to see a Concorde! Not in action of course! =D
The newest addition to the museum at this time, was of course the Space Shuttle Discovery! They've got a pretty amazing collection here!