Innis Arden Golf Club is an 18-hole private golf course in Old Greenwich, Connecticut, built in 1905 and designed by J. Kennedy Tod. It sits in the $$$ (premium) price range for golf in Connecticut. The season runs Apr 1 to Oct 1. Tee times can be booked 3 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.