I'll just add one item to DC, with the caveat that I've never been there in the fall/winter seasons:
The Hillwood Museum. It's full of artifacts collected by Marjorie Merriweather Post, from the Hapsburg Wedding Veil to Faberge Eggs to jade in every color and beyond. Make sure you go to their Tea House, if you indulge. It's a bit more girlie-girl than some other museums, but is truly amazing.
If you have a chance to get to some of the local plantations (I'm a Mount Vernon junkie), try to take in at least one. It puts history into a new perspective. Doing Old Town Alexandria and Mount Vernon on the same day would be good.