More info for you
http://www.nasm.si.edu/museum/udvarhazy/
A cab to the museum from Dulles is $8-12. It's a great place if you like aerospace stuff (such as the Shuttle Enterprise, an SR-71, and the Enola Gay).
http://www.metwashairports.com/dulle...tion/metrorail
In addition to the 5A bus ClimbGuy mentions you can take the Washington Flyer bus ($18 round trip pp) to the West Falls Church metro stop and then ride into town from there. The Smithsonian stop puts you in the middle of the National Mall. There are museums for almost every interest, try this link for info on what's where (
http://www.nps.gov/nama).
Of note, the Smithsonian museums are free (Udvar-Hazy charges for parking but not admission). Their museums are open until 5:30 PM. One museum worth paying for (i.e., not Smithsonian) is the Newseum (
http://www.newseum.org/) on Pennsylvania Ave.
If you are into history, the National Archives (
http://www.archives.gov/dc-metro/washington/) has the Declaration of Independence and Constitution on display and a seasonal ice skating rink outside. For more history, the American History Museum has the Star Spangled Banner. Ford's Theater is a couple of blocks from the Mall and just reopened, their schedule can be found here (
http://www.fordstheatre.org/).
If you want to catch a show at (or just tour) the Kennedy Center, their URL is
http://www.kennedy-center.org/. For NBA/NHL/college hoops/concerts, see what is playing at the Verizon Center (
http://www.verizoncenter.com/). Both are a little ways from the Mall but not too far for a cab ride. Metro can get you to the Verizon Center too but the Kennedy Center isn't close to a stop, a cab or car is the best way to get there. The Spy Museum (
http://www.newseum.org/) is close to the Verizon Center and charges admission.
If you are in town in the spring, the Cherry Blossoms might be blooming around the Tidal Basin (south of the Washington Monument in the opposite direction of the White House). Another good one for springtime is the Roosevelt (FDR, not Teddy) Memorial (
http://www.nps.gov/frde). It is entirely outdoors and is totally different from the big three (Washington Monument, Lincoln Memorial, Jefferson Memorial).
There's a start on things to do. Enjoy your visit.