The Smithsonian Air and Space has a seperate facility out at Dulles Airport that costs to park but is otherwise free.
Free parking after 4, Udvar-Hazy Center is open until 5:30.
http://airandspace.si.edu/parking/It is also a 15 minute walk from Chantilly Crossing Shopping Center if you are feeling adventurous* and want to avoid the $15 parking.
*-intersection from shopping center across US 50 is not the most pedestrian-friendly and neither is the Air & Space Museum Parkway (no sidewalk)
Prince William Forest Park located in Dumfries, VA is pretty good. Loads of trails with all different lengths. Exit 150 on I-95 just south of Woodbridge.
Great Falls. +1
Roosevelt Island - avoid if you aren't getting there early (free parking that goes quickly) or if you aren't biking there, otherwise that place is great
ever since they took C-3PO out of the display case at American History, I haven't been back.........just kidding, all the Smithsonians on the mall are decent
If you want to pay-
Spy Museum and Newseum are good. Spy Museum probably isn't worth it unless you are REALLY into that stuff.
Ford's Theater Walking Tour was very good and fun/interactive for $7.50 (might have been groupon price?). Detective dressed up in period clothes takes you around downtown detailing what happened while you are/were one of the various "eyewitnesses"