The Smithsonian-run Postal Museum is way cooler than you might think. Level 1 has exhibits on postal history from the Pony Express to modern times, where you'll see antique mail planes and touching old letters from soldiers and pioneers. Level 2 holds the world's largest stamp collection. Join the stamp geeks pulling out drawers and snapping photos of the world's rarest stamps (the Ben Franklin Z Grill!), or start your own collection, choosing from among thousands of free international stamps (Guyana, Congo, Cambodia…).
The museum is kid-friendly and hosts story times and card-making workshops. It also has a stamp shop where you can browse the catalog of oddball US Postal Service stamps and have the ‘philatelic clerk’ (excellent job title) fetch your selection. Many of the stamps are hot off the press and aren’t available elsewhere.