North Shore Country Club is an 18-hole private golf course in Roslyn, New York, built in 1920 and designed by A. W. Tillinghast. It sits in the $$ (moderate) price range for golf in New York. The course is open all year. 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.