Just got back from that area, and have been before. We like Taughannic Falls state park
Taughannock Falls State Park - NYS Parks, Recreation & Historic Preservation near Trumansburg (12 miles north of Ithaca), but they do not have hookups. But it is cool at night, so no AC needed. This park was booked, so we had to stay at Spruce Row Campsite
Spruce Row Campground & RV Park - Ithaca, NY. Camping in the Finger Lakes , a large, private campground. Some of the sites are pretty crowded, and it was busy park with lots of kids and a lot of seasonal units (some looked permanent to me). Not my cup of tea, but it did have hookups and shade, and availability.
A must do in the area is the hike through Enfield Glen at Robert H. Treman State .. amazing stone trail through a rocky canyon, looks like something out of elf kingdom in Lord of the Rings! You can access from the top or the bottom of the mountain, I suggest top part and just walk down as far as you like and return by same trail. Treman has campground too at bottom, but I don't know anything about it.