Thanks for the tip on Montauk. There were so many lighthouses on the map along the coast of Long Island that I just picked one almost at random - Fire Island was a place I'd heard of.

I wasn't thinking of climbing any of the lighthouses. Two reasons - a bout of bronchitis has reactivated my asthma and I only have about 85% lung function and I've had bad knees since 1969 when I wasn't obese. I've climbed Key West because I wanted to see if I could see the fort from there (and I couldn't - the pictures I saw that were taken from there must have had trees grow up that concealed it), and the one on Key Biscayne, but that's pretty short. When I got to the top of the Key West one there was a physician who arrived there after me and he looked quite concerned at my general appearance. And that was 3 or 4 years ago.