Parks are fun. You can find a list of them at nycgov.parks.org
Go to Little Italy. littleitalynyc.gov
Go to a burough that you've never been to. I'm assuming you haven't explored them all. If nothing else utilize the MTA's services and get off in a borough you've never visited, take a picture, and then go somewhere else.
I'm really just thinking of free things to do...because thats how I think. Fun things for free are a huge bonus. And NYC offers a lot of them, but you really have to live in the city to know about a lot of the stuff.
"That Sondheim kid has a big future."-Nathan Lane