Unfortunately, any of the MA, RI, or CT State Park campgrounds are almost always fully booked by this time. Earliest weekend date we could find was in mid-September. There are few scattered weekdays here and there.
I believe Island Campground is all seasonal - could be wrong.
Aces High is a very nice choice, another that is within 15 minutes from the ocean beaches is Mystic KOA in North Stonington, CT.
Good luck. Travel safe.
Neil, Lin, and our furry companions, Ashby and Cody. 06 National Surf Side.