BArb,
There are a number of shops surrounding DC but you would need a car for most of them. I think the musuem that was mentioned was the DAR (Daughter's of the American Revolution) musuem. The hotel people should be able to give you directions. You might call them while you are in town and find out just when they are open and if they have any quilts on display. They have a marvelous collection of Baltimore Alblum Quilts but they don't display many at one time. You might be able to arrange a private showing if you call ahead.
Enjoy your stay.