You'll want to do your homework for sure and book ahead of time. We live in southern New England and hit state parks quite a bit. Many in this region are open until the weekend after Labor Day, with a few open until Columbus day or a little beyond. Prime spots in the fall will book out quite a ways in advance for weekends (you shouldn't have a problem getting sites mid week, though), so hop on to the internet as soon as you can for reservations. CT and NH are on reserveamerica.com and VT has their own online booking. I believe ME has their own online booking as well, but we've stayed at a private CG when we have been there near Acadia NP. Don't forget to look for Corps of Engineers camgrounds as well on recreation.gov, there are some good ones in the region!