if you’re avoiding cities (may not be a bad idea with a car in the northeast):
North Carolina: Outer Banks is nice, but a heck of a trip if you’re in a rush. Requires at least two days to enjoy.
Virginia: camp in Appalachia. Good way to spend a night.
Maryland: eastern shore of the Chesapeake. Try to go boating.
Delaware: beach near Lewes (nearby is a ferry to Cape May, New Jersey).
New Jersey: the Shore is the best beach option.
New York: has some of the best wine country in the USA; the beaches are okay, but they’re better further south; great railroad tourism around NYS too.
For cities within that range, the Smithsonian in DC is very much worth a visit. Great museums, and they’re all free try to visit the Baltimore Aquarium and waterfront. Philly is nice, but my experience with it is limited to the Americana exhibits.
NYC is definitely worth visiting, but can be rough on the budget and the stress level with parking. It’s probably the art capital of the world, and many of its museums probably trounce the already very good ones you find in D.C.. This may have changed since I last visited, but keep in mind that many of the better museums look like they’re charging you, but the charge is really a “suggested donation.” If you’re on a budget, try getting a hotel in Jersey City that’s near the PATH train.