The Watkins Glen KOA is pretty good but crowded when there are races at Watkins Glen. Camp Bell is a nice little campground and not far from Corning.
If you are willing to give up full hook ups, Sampson State Park is really nice and has an interesting history as a military base. As mentioned above, Letchworth SP is a great park but not as close to some of the finger lake areas. And the Watkins Glen State Park is nice. We used to live in western New York and enjoyed many trips to the finger lakes area. If you want to treat yourself to something special, take a hot air balloon ride that takes off from Letchworth SP......absolutely awesome! And be sure to hike the gorge at Watkins Glen and tour the Corning Glass Works. Enjoy!