Montauk is a summer destination for the NYC crowd. Those who have the means can rent beach accomodations and spend days eating fresh seafood and bumming on the beach.
Its a long drive thru the fabled Hamptons to get to this outpost. Also home to Camp Hero, now a state park and previously home of the Montauk Project which may or may not have been experimental time travel research.
Its a great area to explore and perhaps the only place near NYC where you can get reasonable sunset shots from the beach.