I hadn't realized, as I occupied Room 502, that the lovely lawn I was looking at out the back windows was a hidden graveyard. There are no headstones, but plaques set into the ground, and is called the New York Marble Cemetery. It's the oldest non-religious cemetery in the city.
You can get in (through an alley accessed from Second Ave) on the 4th Sunday of the month, from April through October.
I'd thought it was an unnaturally unoccupied little park!