Tim, plan your trip and check for CG's along the way. Many of the CG's close after the Labor Day weekend. Some stay open until October. You need to check, or look for Walmarts. As stated, you most likely will not have a problem during the week, but weekends and holidays can be trying on the nerves. Also, special event days in local areas.
We have stayed at the Freeport/Durham KOA in Maine. It is about 6 miles from the L.L. Bean Home Outlet Store. I forgot where we stayed in New Hampshire, but I used the GPS to get to Freeport and I was on some roads that were pretty crooked, but we made it. Sometimes at 25 mph.
I hope you get to Newport, RI. There is a lot of history there and the Mansion tour (Self guided) is great. We went to 8 mansions in a two day span. About $60 bucks a person, but see if you can get the Senior's rate[
]. If you do spend a few days there, go down to the pier around 11 a.m. and get a couple lobsters for $8 apiece. Back at the Monty, throw them on the grill.
There is a place about 20 miles out of Newport gong toward the Block Island Ferry. It is Firsherman's State Park and Campground. Nice and quiet - or so it was.