I will be repeating probably what most others have mentioned.
In MD assateague state park is a must stop, even better if you can get a site in the sought after electric loop. Book now, who knows you might get lucky.
In NY, Letchworth State Park and Watkins Glen state parks were rated the top 10 in the USA. This said we enjoyed Watkins Glen better as Lots to do around scenic Seneca lake besides Watkins Glen Gorge. Cooperstown if your a baseball fan is a must. Lake George area, maybe take a day trip to Ausible Chasm.
NH, Licoln/Woodstock area is a great home base and centrally located to exploring all of the White Mountain Attractions
RI, Fisherman's Memorial Campground in Narragansett is another great homebase for exploring Newport RI & Mystic Seaport CT. Take the ferry down the street and visit scenic Block Island or enjoy the local beaches.
MA, Cape Cod is a must visit. I would strongly suggest booking just after Labor Day as traffic is just awful. Alantic Oaks Campground is at the halfway point up the cape and gets very good reviews. Watch out for the sharks while swimming! (I'm not Kidding as they have had problems)
ME. Acadia NP
VT, Our personal Favorite is
Winhall Brook in South Londonderry, lots of country charm at the campground and in the area. Also suggest the Lake Champlain Area in VT,
Champlain Adult CampgroundHope this helps! :C
Mike