This is the fourth-oldest active lighthouse in the US, commissioned by George Washington and built in 1796. It's a nice climb, but the 15-person limit may involve a wait and a test of one's claustrophobia limits. The payoff is the view, which stretches to the eastern horizon. Suffolk County bus 10C heads here from East Hampton and Montauk.
It's also at this point that the slave-ship Amistad (focus of the film of the same name) first came ashore in America, prior to the famous trial in New Haven.