Arlington Cemetery. Vietnam Veterans Memorial. Korean War Memorial. Lincoln Memorial...
Not so much Arlington, but war memorials, Washington Monument, et al are all within easy walking distance. Call your representatives and see whther they can arrange anything for you- special tours, tix, or whatever.
Btw I'm told that the most effective way to see many of these attractions is at night.
Definitely Arlington National Cemetery; especially if it's cherry blossom time, you'll see trees as beautiful all over the cemetery as you will in any of the more congested spots, like around the Tidal Basin.