Unexpected surprise near Boston
Less than 25 miles north of Boston and <5 miles from the interstate, Lorraine Park campground at Harold Parker State Forest provides ample on-site activities and also serves as a jumping off point for exploring the Massachusetts coast north of Boston or a stop en route to NH and Maine.
Every site seems to have its own water spigot, though it's not necessarily conveniently located if you want to hook up a trailer/RV. There are 11 sites with water/electric. Sites are large, often with good separation from neighbors, some have a hilly approach. The reservation website doesn't provide pictures, so I've tried to capture most here. Some of the sites are large enough that if you have a small camper or van you may be able to pull through. They've designated more than half the sites as tent only. There's a great playground area and also basketball and volleyball courts, but in this COVID-19 era, don't expect them to be open in 2020. I heard a little road traffic around the perimeter, but not much.
Bring a bike, pack some sneakers or hiking boots, toss in a swimsuit or a fishing pole, and explore! There are miles of trails and logging roads for hiking and biking. A small beach is within walking distance from the campground (wildflowers bloom in the area in late May).
Nearby national park sites include Lowell, Minute Man, and Boston where you'll learn about the industrial revolution or the American revolution respectively. Concord will introduce you to some early American authors; Salem Maritime, Saugus Iron Works, Essex National Heritage explore other aspects of the area. Head to Gloucester for a whale watch or wander the coastal towns.