There is tons to see & do in NYC. Check out the websites to help you plan.
Not sure how much time you will have, as that will help with planning.
At the pier there is no luggage storage space that I remember. Always a problem. And you do not want to go all the way to the airport & back.
Again, timing. IF you have all day until leaving you could look into a day rate at a hotel near the pier. There is a Best Western that used to offer this. That way you can store your luggage & even have time to freshen up before your flight.
There is an On & Off bus available for tours.
I have friends from the UK who loved this.
You can do helicopter rides, or just walk around.
Good Luck & enjoy your cruise.