When in October?
Columbus day weekend in particular will be busy (very busy) with leaf peepers clogging the roads etc. Depending on the year, it could be very pretty peak foliage, or it could be early or late, but that's very likely to be the busiest weekend regardless...one of the busiest of the year. Very soon after that (often the next day) many campgrounds will be closing or thinking of closing.
I haven't done a lot of research, but if it were me I might go for one of the campgrounds along the Kancamagus highway--forest service campgrounds, so very, very limited amenities and no hookups.
