When is your cruise? You can stay at any hotel in NYC, if you want to be "where the action is", you can stay in Times Square.
Let's see, if you are coming in the summer, Central Park would be something to see. But go in during the day, don't go in there at night, its dangerous & I'm not kidding. Make sure during the day you are around people in there.
Statue of Liberty if you are into any historical monuments. The Circle Line is a ship that goes around the city of NY - unless you'll be sick of being on a ship by then, . Or go to the top of the Empire State building to see the entire city in its glory. Careful - its windy up there!
Museum of Natural History is pretty cool. Go down to Wall Street if you wish to see where the Twin Towers once stood (my office building was directly across from them, got to watch the cleanup).
If you are into shopping, there's some good shopping on 8th avenue, if you have the $$ to boot or just want to see how the rich live. You may even see a star or two shopping.
Broadway plays abound! Get some theater tickets if there's a particular play you want to see. Hope this helps!!
Serenade of the Seas - '05
Sovereign of the Seas - '07
Can't help you out with the hotels in NYC, but depending apon your budget, you can get a great deal on a room in the location of your choice by bidding for it on priceline. As far as attractions... by day I would do the NBC tour/rockfellar cntr, 911 memorial site, and the Statue of liberty and at night, the Empire State Building and Times Square. To save money on parking and transportation, I would suggest that you check out gray lines hop on-hop off manhatten bus tour---its just around $50. per person for 48 hours of use and if time allows theres many more attractions around these, that are low cost.