The Merchant's House Museum is another favorite place of mine:
It's another NYC place that is rumored to be haunted. But unlike St. Mark's, there is serious evidence to back this up. Definitely visit when they are giving a guided tour, the volunteers who run the tours are passionate about the building and you'll learn a lot more than you would if you tour the building on your own.
I took one of the candlelight ghost tours here in October, and it was seriously spooky. (although we did not encounter any actual ghosts) At the end of the tour we could enter a raffle: the winner would get to spend a night in the house with some psychic researchers who were going to try to make contact with the resident ghost.