While you're there, check out the Shagwon Bar/Grill, it's the local/townie joint on main street.
Also check out the Memory Motel, the Stones wrote a song about it
The Memory Motel is in Montauk on Long Island. It's near The Church Estate, which Andy Warhol bought in 1972. According to Arthur Schneider, who owns the Memory Motel, The Stones stayed at Warhol's estate when they were on tour in 1975-'76. (They were good friends with Warhol, who designed the Sticky Fingers album cover.) Since the Memory Motel was the only place in the area with a pool table and a piano, The Stones would occasionally come by and hang out at the bar. The owners at the time were not impressed - they hated The Stones.