The Smithsonian's National Air and Space Museum, located on the National Mall, is one of Washington, DC's most popular tourist sites. Dedicated to the wonder of flight, the museum features artifacts from both air and space travel, including spacesuits and capsules, war planes, rockets, and Charles Lindbergh's Spirit of Saint Louis, which is dramatically suspended in the main lobby. It's fun, free, and entertaining for all ages. But it's only a fraction of the Smithsonian's air and space artifacts.
A few miles outside of Washington, DC, near Dulles International Airport, is the Steven F. Udvar-Hazy Center, the Smithsonian's other National Air and Space Museum. Unlike its downtown counterpart, the Center has the luxury of land, and therefore displays many larger air and space crafts, including a NASA space shuttle and, my personal favorite, an Air France Concorde.
Even if you're not normally someone who gets excited about airplanes, you can enjoy this museum for the sheer impressiveness of its size and the size of the crafts. It would be difficult to walk under a space shuttle and not be awed by its largess. You'll also see the Enola Gay, infamous for dropping an atomic bomb on Hiroshima, early aircraft from the Wright Brothers era, and the world's fastest jet-propelled aircraft, the Lockheed SR-17 Blackbird, which made its final voyage form Los Angeles to Washington, DC in 1 hour 4 minutes and 20 seconds (2,124 miles per hour). In short, the other Air and Space Museum is even better than the one that gets all the attention on the Mall.