The National Postal Museum is a Smithsonian Institution Museum devoted to the history of the US Postal Service.
I honestly LOVED this museum. I thought it was engaging and the exhibits were interesting. I would say take older kids (6+) as there is not a lot of play-type areas. I liked the old postal vehicles you could climb inside and there is a cool tunnel thing you can go through as well. There are exhibits where you take pictures and make postcards and mail them from right there. It's not huge, and never crowded, but I would recommend it on a high-traffic day rather than hitting up the Smithsonians. There are some cool rooms with stamps all over the walls too.
We enjoyed this museum. It was nice to take a look at the history and how far we've come since the post office started. They have a wide variety of stamps, including nonconformities, and there were a couple reenactors as well. I definately recommend this for anyone considering a stamp collection, or just interested in history!