The Jazz in the Garden is one of my favorite things to do. Every stitch of grass and ground is taken. People bring blankets or chairs, picnic baskets, etc. You can buy beer or sangria. The only question is the weather (rain...or sometimes it gets hotter than shit). Great people watching...and always hot ass there!!
Arlington Cemetery is one of my favorites. I usually go thru the back gate on Ft. Myer (since I am military I can get in that way)...but the front is fine too. You can walk through General Lee's house, check out some cool grave sites (JFK), and see the changing of the guard at the Tomb of the Unknown Soldier (really, really cool to watch).
Of course, The Mall is awesome. Lots of kids/tourists in town right now though (the end of the school year trips). They are still working on the Washington Monument, which was damaged in the earthquake 2 years ago.
The DC/Washington Zoo is free and very nice.
The National Cathedral is nice.
Baltimore isn't too far, the Inner Harbor area is fun to go to.
Air Force Memorial is okay...near the Pentagon (where the 911 Memorial is).