The top golf courses in Lake Placid were designed by Craig Wood, the US Open champion, and Alister MacKenzie, the famous architect of the Golden Age. These are Craig Wood Golf Club and Lake Placid Club Mountain Course respectively.
There are public and private golf courses in Lake George, Saranac Lake, Indian Lake, Tupper Lake, Schroon Lake, Warrensburg, Bolton Landing, Stony Creek, Ticonderoga, Peru and many others. Pro shops and rentals are available in most of them.
The list of all NY golf courses with ratings is available here