Montauk Downs State Park. The Robert Trent Jones–designed golf course at Montauk Downs State Park is one of the top public courses in the nation. It's nestled among rolling hills surrounded by four bodies of water, which creates ever-changing wind currents that can change the way the course is played day by day. It's a busy course, so call at least a week in advance in summer to reserve tee times. The Downs is off West Lake Drive, near the harbor. 50 S. Fairview Ave., Montauk, New York, 11954. 631/668–5000; parks.ny.gov. $86–$96 visitors; $43–$48 NY residents.