Hi DoneItAll and Welcome to the RTA Forums!
If you plan on going as far north as Plattsburgh, Pointe Au Roche State Park is a beautiful park located right by Lake Champlain. They have a very nice beach, large pic-nic areas and a well maintained bicycle path.
If you visit the Lake Champlain Islands, North Hero State Park is a great place to stop overnight. If you enjoy canoeing or kayaking, paddle accross the lake to Knight Island State Park and then to Burton Island. Burton Island State Park is also accessible by ferry. These are not technically in NY though but they're worth a visit.
I'm usually not very fond of big commercial campgrounds but I thought the KOA in Ausable Chasm offered more privacy and is conveniently located near Mt White Face hiking trails and not too close to the freeway.
Here's the NY State Parks website. I don't think they succeeded in making this website user friendly though but maybe it can help you locate certain parks.
Happy planning!
Gen