One of the most popular museums in the Smithsonian collection is the Air and Space Museum downtown. Unfortunately, it's rather difficult to land a space shuttle on the National Mall.
However, it is easy at Dulles Airport. So the Smithsonian put all the really big and cool aircraft out in the Virginia suburbs, at the poorly named big donor Udvar-Hazy Center. The SR-71, which flies so fast at such a high altitude that it actually stretches. Yes, there is a Space Shuttle and other collections of big (and really small) aircraft, engines, and another Imax theater.
One of the highlights is the ability to go up in the tower and watched the airplanes at Dulles come in for a close landing.