According to google maps you are approx 9 hours from Foxwoods casino in CT. The native American museum nearby is outstanding. No wonder I thought the statues looked so realistic, hands and faces were cast from real people. You can include a visit to Mystic Seaport. There's also a nearby small but interesting natural science museum. I visited years ago but still remember the little room where you could experience a meadow at night. https://dpnc.org/

Not really on your list of ideas but closer to Virginia Beach would be Frederick MD. Google Community Bridge. The trompe l'oeil paintings on the sides of buildings surely would fascinate any age. Friends and I argued about one, whether an open window was real or not. They voted real. It was painted. There are a lot of fun little shops and maybe there's a bookstore. You might also check to see what's going on at a library. Your children are the right age group for story hours.
Perhaps Havre de Grace MD for small museums and lighthouse. We enjoyed a winter weekend there once.

Does it have to be on the coast? The idea of an Indian visit could be Cherokee NC and Great Smoky Mountain National Park.
Winston Salem, NC at Christmas is wonderful with a lot of music offered at Old Salem--sort of a miniature Williamsburg..
When do you want to do this?

New England would be an obvious option. You could do a few nights in Boston - lots of history, dining, museums, etc. You could then stay on Cape Cod - amazing beaches, nice little villages, bike trails, etc. You could also do the Maine coast, and even visit New Hampshire's White Mountains,and Vermont's Green mountains. For something really different, you could even do French Canada - Montreal and the Eastern Townships - however, this is probably 11-12 hours from you.

Boston area
Museum of ScienceBoston Children’s Museum
New England Aquarium
Freedom Trail

Not in town:Plimouth Plantation in Plymouth MA
Old Sturbridge Village in Sturbridge MA

Philadelphia area
Please Touch Museum
Franklin Institute
Philadelphia Zoo
Independence Hall
Get a Philly Cheesesteak (be sure to order “wit” or “without”)

Savannah and Jekyll Island. Split your time between the two.