The National Postal Museum. I'm sure you've never been to it, probably not really heard of it, but it very well may be my favorite of the Smithsonians. It gets short tourist shrift because it's not on the National Mall (probably contributing to my love of it because it's never crowded) and it's not very big. And, when people think about it, they don't really want to go to a museum that is about the mail. Who cares? You should.
It covers the history of mail delivery from the very beginnings of the colonies to how we deliver mail today. There are lots of great interactives, from timelines to a stagecoach you can climb into. (See above.) I learned that there were never ponies used in the Pony Express--shocking, right!? And tons of other really fun things can be learned, usually with a hands-on component.
If you can't get to the museum, they also have one of the most informative websites I've seen. Not always completely interactive, but you can learn how a family mailed their daughter to her grandparents because it was cheaper than buying her a train ticket. Plus, if you're into stamps, they have some very nice examples.