Going to NYC in the spring, any ideas of things to do off the beaten path?

I live in Upstate NY and sadly have never been to NYC! I think I want to go in the spring when the weather gets a bit better and I am looking for some things to do that aren't the traditional touristy stuff (i.e. seeing the statue of liberty, Empire state building...that stuff is easy to figure out) Even websites with some ideas you think are good would be of a great help.