The Supreme Court
Inside they have two stair cases like this. We walked around looking and ate breakfast in the cafeteria there. (I don't recommend)
I had hoped to get on one of the tours that they do in the court room, but we missed it by a few minutes and the kids weren't terribly interested in staying longer just to go in the court room. I went in on the tour about 7 years ago and it was very interesting. It's by far the best part of going there.