I've camped at Lake Taconic many times and I really like it. The fishing is good to if you're into that. You can rent a boat there. And it's an easy drive from NYC up the Taconic Parkway.
Pretty much with any of the NY State parks you can't go wrong. But if you are going to camp in the Catskills be prepared to bear proof the campsite at all times. That means keeping all food and cooking items locked in the car at all times.
Campgrounds and Camping Reservations - New York State Parks
This site has a list of all the parks and you can make a reservation on line.