Nobody mentions Arlington National Cemetary when they talk about visiting DC.
Its a shame because you will be very moved by the hushed atmosphere and the respect that even tourists show when walking about this place.
Take the guided tour tram things if you don't have a lot of time because its a hike from the parking area to the main stuff you want to see. (kennedy, unknowns, etc).
Or you can walk around and see cool monuments and gravesites from the Civil war era to rows and rows of perfectly alligned crosses. Even see funerals that are going on today with the distant gun fire that will give you goose bumps.
Will give you much insight and respect for the sacrafices made over the years as an american.