The 150-foot cliffs along Mohegan Trail, the island's southernmost road, are named for an Indian battle in which, lore has it, the local Manisses pinned down an attacking band of Mohegan Indians at the base of the bluffs. From the top of the bluffs you can see Montauk Point, on Long Island, N.Y. At Payne Overlook, just west of the Southeast Lighthouse, a remarkable set of stairs descends to the beach below. (The overlook platform is closed because of erosion problems.)