Very cool. I love museums.
You should spend a week in DC at the museums.
There are about 12 or 13 in DC alone and free with huge numbers of programs.
There are multiple private, good museums - Corcoran, Renwick, etc.
There are also the specialty museums which are a must see, like that National Museum of Health and Medicine, the Holocaust Museum, the Newseum, there is an unending supply of stuff to see.
Best time is now - fewer tourists, fewer crowds.
Worst time is June, July, August, Sept. enormous crowds, hot
If you like art, the West wing of the National Gallery is wonderful, not as big as the Met in NY but more concentrated. Cameras are OK, tripods are not.