The rocks by the lighthouse. The place I take all of my Montauk visitors. I absolutely love being out there.. watching the waves crash mere feet away, the smell of the ocean surrounding us. It doesn't get much better. Even when it's cold and we need gloves, hats, and scarves.
Also, if you were wondering.. you can feel totally free to go surfing out by the lighthouse.. but only in the dead of winter. We enjoyed that sign.