So, now that the trip is over, thanks for all your comments and suggestions.
We didn't have much time, and also, my wife has been nursing a broken bone in her leg for months, so we didn't get to do much.
Here's what we made it to, in order of visitation:
- Arlington National Cemetery
- Smithsonian Air & Space
- Smithsonian American History
- International Spy Museum
- Smithsonian Portrait Gallery
We had planned on Ford's Theater, but it was closed to entry by the time we would have gotten there (after watching Guardians of the Galaxy). I wanted to do some other things, but my wife's leg was really bothering her. Also, I didn't even get to log a single geocache on the entire trip.