Possibly the best thing about Washington D.C. is that the National Gallery of Art (along with, I think, all the Smithsonian) is free. This means you just take a casual stroll through without any of the pressure of having spent a sizable sum like you might to visit a place like the Art Institute in Chicago. In Chicago a visit is an event, you need to see the Seurat, the Grant Wood, etc. You've spent money and you need make it count.
In D.C. you can literally walk in, go look at the big Joan Mitchell for 10 minutes and continue on your day. Or you can wander through a room you've never been interested in and find something and then go to lunch. Without the commitment to get everything done, you are suddenly free.
Good libraries (edit: even mediocre libraries) also have this quality.