The National Air & Space Museum is so awesome they made an attic for it: the Steven F Udvar-Hazy Center. Highlights include the SR-71 Blackbird (the world's fastest jet), space shuttle Enterprise and the Enola Gay (the B-29 that dropped the atomic bomb on Hiroshima). Visitors can hang out in the observation tower and watch the planes take off and land at Dulles, go on a simulator (piloting a jet, taking a space walk), or catch an IMAX show
Free 90-minute tours through the collection are offered at 10:30am and 1pm daily. To get out here, take the Metro Silver Line to Wiehle-Reston East station and transfer to the Fairfax Connector bus 983 one stop to the museum (you can pay $1.75 cash or use a SmarTrip card on the bus). If stopping in from Dulles Airport, you can bus it (again the Fairfax Connector bus 983) or cab it (about $15). If you're driving, take I-66 West to VA 267 West, then VA 28 South, then follow the signs. Parking is $15 (free after 4pm).