Eighteen Hole Course at Maidstone Golf Club is a 27-hole private golf course in East Hampton, New York, built in 1891 and designed by William H. Tucker. It sits in the $$$$ (splurge) price range for golf in New York. The season runs Apr 1 to Oct 31. Play is generally limited to members and their guests.
Details like fees and seasons change, so call the course before you head out.