June 6, 1985 Unknown Eater: Red Sails Inn. When producer and Unknown Eater Eileen Brennan had visitors in town, she liked to take them to the less obvious restaurants—Red Sails Inn on Shelter Island was the perfect place. Fresh seafood was on the menu daily—and plenty of choices. Entrees cost around 11 dollars. All that with an awesome view of the bay in the back. The rustic restaurant was 40 years old in 1985. It closed in 2016—a long run for a special restaurant locals loved to take their out of town guests to.