Traveling through upstate NY

Especially if it's not a weekend, I suspect you could get a site at most of the New York state parks at that time of year without a reservation. They don't require two night's payment for a single night of reservationless camping. You can check periodically online and see how many sites are reserved as time goes on and gauge somewhat from that how crowded things are going to be.

Another alternative is to choose a park you'd like to spend a day or two at and stay a bit longer. Letchworth is one good example that's in the general vicinity of your first night's desired driving distance...though maybe a bit on the long side.