Make reservations, preferably soon.
New York has some nice state parks if you don't mind comparatively rustic camping. Letchworth and Watkins Glen state parks are two that I've camped at that have some fun hiking/walks for children (and others), though they'd probably be a little on the crowded side during leaf season. Indeed, that's true most anywhere you'd be camping. Stony Brook state park also looks like it could be fun, though I have not been there myself as yet.
Knoebels (a bit further south, in Elysburg, PA) is great. Their Lake Glory campground has larger sites than the Knoebels campground, in general, but is less convenient to the amusement park as you have to take a shuttle bus or drive to and fro. The sites in the Knoebels campground tend to get larger the further up the hill away from the rides you get. Take note of their operating days and events for that time of year as it's past the regular operating season.
