There's a whole lot to see and do around these areas!
Cities and cultural areas: Washington, DC could keep you busy for months with the various museums (many free), memorials, the National Zoo, etc. (I've stayed at Greenbelt NP, which is maybe a half hour or 45 minute walk from a Metro station and very affordable.) Highlights for me include the zoo, the Air and Space museum annex at Dulles Airport (many, many more historical aircraft on display than at the main air and space museum), and some of the art museums. The National Building Museum's free tour was interesting, too, giving the history of the building it's housed in.
Philadelphia--many historical sites, the world-renowned art institute, performing arts...while I haven't visited there with my RV, if I did I would probably stay at the Campus Park and Ride.
NYC--also enormous, with museums, arts, gardens, zoos, etc. to fill many many days. There are a number of threads here on places to stay near NYC (and most other major cities), probably the most convenient overall being Liberty Harbor across the river in New Jersey. I've stayed at Floyd Bennett Field, which is not the easiest to get to with an RV (being in Brooklyn), but is affordable and reasonably accessible to public transit.
Boston--historical sites, museums, the New England Aquarium...avoid driving in Boston if at all possible, particularly with an RV. Driving under Boston via the big dig is not too bad, at least if you avoid rush hours, but hazardous materials including propane tanks are not permitted in the tunnels.
If you like theme parks and amusement parks and roller coasters, there are many fine places to stop. Knoebels (Elysburg, PA) is probably my overall favorite; it has a wonderful vibe, and the campground on site is exceptionally convenient and well run, though not exceptional as a campground (smallish sites--some very small, modest landscaping, utilitarian but clean and functional restrooms, etc.) Other decent amusement parks of varying sizes include Kennywood (outside of Pittsburgh), Hersheypark (Hershey, PA), Kanobie Lake Park (Salem, New Hampshire), Lake Compounce (Bristol, CT), and Rye Playland (Rye, NY, unusually owned by the city), among others.
Natural areas: Letchworth State Park in New York is a must-see, one of the very nicest state parks anywhere. Watkins Glen (the state park with the glen itself) is neat, too. Acadia (note: no "r") is lovely, as are the White Mountains generally of New Hampshire, and indeed many places in the region. Hiking trails abound throughout the Adirondacks, the Green Mountains, the White Mountains, etc...some quite long distance trails (such as the Appalachian Trail and the Long Trail). There are many places to bike or canoe as well.
Other sites and things: If you like baseball, spending a day or two at the Little League World Series is well worth the effort. There are some fun minor league teams and ballparks, as well; I'm naturally fond of the Vermont Lake Monsters and their home park at Centennial Field, which is an older ballpark than any major league stadium.
The Shelburne Museum is a great stop, which its eclectic (and extensive) collection of generally folk art related things, very broadly interpreted. Mystic Seaport has a world-class collection of boats.
That's probably long enough, though it just starts to scratch the surface. If you share some of your particular interests, that would help a lot in recommending specific things.