Some of the high points in New England you may want to consider on your 15 day Northeast Trip. and as mentioned,
ME, Acadia, 3 days a least
NH, Licoln/Woodstock area is a great home base and centrally located to exploring all of the White Mountain Attractions, 3 days at least.
Lincoln/Woodstock KOA gets good reviews
MA, Boston
Boston Minuteman Campground We have never stayed there as we live close enough to drive to boston but I hear campground is very popular stop for the Rvers that tour the Boston area. Maybe 2 or 3 days.
Cape Cod IMO is better visited during off season as traffic can be tough during the peak summer months but if you want to give it a try I would recommend
Atlantic Oaks Campground which is at the halfway point up the cape and gets very good reviews.
ME, Old Orchard Beach (OOB southern ME) your kids will love this stop as area is very touristy, family oriented and has lots and lots of stuff for teenagers. Check out
Bayleys Camping ResortJust another FYI, beach water temps in New England will be for the most part be to cold for swimming at the time of your planned trip
Hope this helps
Mike