Garden City Country Club is an 18-hole private golf course in Garden City, New York, built in 1916 and designed by Walter Travis. It sits in the $$$ (premium) price range for golf in New York. The course is open all year. Tee times can be booked 2 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.