Back in the late '60's I traveled all over the US by Greyhound bus. It was great.
You might try googleing US quilt shows to see if there is one near where you will be at the time you are here. Also check to see about quilting museums. Then check to see how long it takes to get from point A to point B. The Greyhound bus sight tells the # of hours involved in the trip. Then you would know if you needed to get a hotel room for a night once you arrive.
Washington DC has so many museums it would take weeks to see them all. The Smithsonian has several in the DC area.
hope this helps a little.