I live and work in the DC area. Don't come to the DC area in June, July or August. Way to crowded, and way to hot and humid. As the others have said, April and September/October are more tolerable. The last few days were pleasant. I go to Ocean City in early November and get some nice warm days. Mid November to start of April - not so much.
Bring your walking shoes, because you will be doing a lot of hiking around the Mall. Most of the stuff around the Mall is free. Go over to Arlington and catch the changing of the Guard at the Tomb of the Unknown Soldier. The pilgrims seem to like the Cherry Blossom Festival in late April. Guess I am not sentimental or romantic enough to get it, but they say it is something to see.
There is the B&O train museum
clicky just up the road in Baltimore.
The East Coast is a big place. And the drive across the country is pretty long. Don't get to ambitious. There is enough in the DC area to burn up your whole vacation.