The Chequit is a rambling inn perched on a slope in Shelter Island Heights. It has a big bar, a patio, and porch on the second floor. You can look out across Dering Harbor from much of the room, which contains a dartboard and a pool table. The menu is tried and true American with a Southwestern influence, concentrating on seafood and local fresh produce. There is a roast Long Island duck with citrus melon glaze and several vegetarian options.