The Muttontown Club is an 18-hole private golf course in East Norwich, New York, built in 1959 and designed by Alfred H. Tull. It sits in the $$$$ (splurge) price range for golf in New York. The season runs Mar 1 to Jan 31 (closed on Mondays). Tee times can be booked 7 days in advance. Play is generally limited to members and their guests.
Details like fees and seasons change, so call the course before you head out.