This Greenport legend was the nation’s oldest restaurant continuously owned by the same family (the Portuguese Claudio clan; since 1870) until 2018 when it was sold to three Greenport loyalist families who have carried on its mostly seafood-heavy traditions with a modern upgrade. Dishes include swordfish ragù, spaghetti with clams, fresh oysters and dry-aged steaks (from Kansas).
For a more casual meal and an epic outdoor bar, hit Claudio's Waterfront on the nearby pier (mains $17 to $26).