A few weekends ago a friend & I went to the National Postal Museum, based primarily on the fact that it was a museum we had never been to before and my interest was piqued after reading a review on Oh So Beautiful Paper. It was definitely a lot more interesting than most people would probably expect; I highly recommend checking it out if you're in the area!
You can create your own instant stamp collection which was pretty awesome; these are the ones I got.
The museum is really easy to get to since it's right across the street from Union Station, which also seems to have gotten way bigger than I remembered. So if you're there waiting for a train, there are lots of places to kill time!