There are lots of campgrounds around the Finger Lakes area but it is hard to find one right on the water. Sampson State Park in Romulus, NY is on Seneca Lake. Sampson State Park - NYS Parks, Recreation & Historic Preservation
Here is a link to a listing of campsites around the Finger Lakes: Finger Lakes Campgrounds â€“ Camping Options in the Finger Lakes of NY
I will be camping at Spruce Row Campgrounds next weekend near Ithaca, NY which is at the end of Cayuga Lake but a vehicle is needed to get around in because it is a short ways from the lake. I live near the Finger Lakes so if you have any questions, send a PM and I'll try and answer them for you.