NY State parks are pretty nice, if you can live without full hookups. Many sites are spacious and offer reasonable privacy. On your way from Ohio, I recommend stopping at Allegany State Park. There are two sides to this park: Red House (by far the most scenic) and Quaker. The campground at Red House is treed and gets a bit smokey at night with a campground full of fires. Quaker has both treed sites and open sites. I prefer the open sites at Cain Hollow (loop A). Neither side gets great marks for bathroom cleanliness, but they are usually tolerable.
My two favorites in the Finger Lakes are Keuka Lake State Park and Sampson State Park. Both get high marks for restroom cleanliness and site maintenance. As a poster above noted Sampson is great for biking, especially if you are old and chubby like me. Lots of flat roads remaining from its days as a military training base. There's also a nice state park in Geneva with a pleasant tree lined lane along the end of the lake - a great walk or ride.
Keuka Lake State Park is also very nice. Lots of privacy in most of these sites. The Management, however, is really uptight compared to other state parks I've visited. YOU WILL LEAVE AT 11AM and YOU MAY NOT CHECK IN UNTIL EXACTLY 3PM. No kidding. I arrived at 10 minutes to 3 and they made me wait. Other than that, they seem fairly reasonable and take good care of the park. In the same vein, the other two parks will let you check in early if the site is vacant and won't get there hair on fire if you're a little late in leaving.
If you stay at Keuka Lake State Park, I recommend Timmy G's as a good place to eat. Real food as opposed to the nicely decorated stuff with names you can't pronounce and quantities so small the proprietors should be embarrassed - but they're not. But I digress. It's located in an alley adjacent to TOPS grocery (the only one in town).
A word about Watkins Glenn - I found the maneuver room in the state park campground to be somewhat limiting. Also check for events at the track. Watkins Glenn traffic is horrific if there's a race or other event.