Train to Washington DC. Weather will be mild as it's not too far north to really be chilly yet, but past the hot period. Fall rains should be started yet. See the Smithsonian Museum and then go from there.
Second on the train to DC - we went from DC to NY on our honeymoon via the
Acela Express - nice fast train and lots of fun. PS: you can stay in NY for less than $200/night if you plan well. You can stay in a nice hotel within a block of the subway in Queens or New Jersey (easy access to Manhattan) for ~$100 or so as well.
LOTS to do in DC - highly recommended. We'd move there if we moved anywhere other than Texas
Smithsonian, all the landmarks. About the only thing you can't get into on short notice is the Capitol and White House. You'd need at least 4 months notice to do the capitol, and a few months more for the white house.
