Unpopular opinion: the Air & Space Museum on the National Mall is... meh. The exhibits are nice, sure, but it was SO PACKED in there it was muggy inside from all the people bodies squished together. Ew.
The Udvar-Hazy Air & and Space Museum by Dulles, on the other hand, was AMAZING. The second we walked in the door, Paul noticed, "This one is nice!" The very nice old volunteer at the info desk suggested we take a lap around over the catwalk, through the shuttle hanger, before joining a tour. (Always listen to the suggestions of nice old volunteers, they know what they're talking about.) A docent led us on a nearly two hour tour through aviation history. I'm not actually a big airplane person, but I love stories, and this guy could tell stories.
Highly recommend the museum by the airport. There's even a Shake Shack inside! Admission is free, $15 for parking.