There are only four outdoor phone booths left in Manhattan - and they're all on West End Avenue. That's it: four.
This one is at 101st Street:
This is at the corner of 100th Street:
This tree-shrouded booth can be found at the corner of 90th Street.
Finally, this is at 66th Street.
And that's it.
Sure, there are phone stands - posts with a payphone attached and zero privacy. But those of the four-walled variety are at the top of the near-extinction list.
If you happen to pass by, I seriously advise you to stop in one of these booths while they're still around. Note that someone still cares enough to keep the overhead light in proper working order. Close the door (be amazed that they even have doors), and you'll find yourself in a veritable fishbowl plunked down in the center of Manhattan. The walls actually keep out a good amount of sound, and it's surreal to look out at the world around you with something you don't usually get on a busy Manhattan avenue: personal space.
PS - This site has tons of pictures of phone booths, both from New York and throughout the world, for anyone interested. Forgotten-NY has a great article on other rare phone miscellany around the city.