If you don't mind spending $20/person the Newseum is one of my favorites. The national portrait gallery is also pretty great, and is right by the spy museum if you end up going there.
I definitely recommend visiting the Washington monument, WWII memorial and Lincoln memorial at dusk. Mainly because it looks amazing at that time, but also because there are not nearly as many tourists & it's not as hot. pDunc also suggests you go to the zoo to see the monkeys!
Another cool music option is Jazz in the sculpture garden, which happens every Friday night.
As far as vegan options, I highly recommend sticky fingers! It's an awesome bakery in Columbia heights. All of Holland's options are pretty great as well. Selam is a really good option for Ethiopian food.