I live in "Cape Liberty" aka Bayonne, New Jersey. The Royal Caribbean website is sending you quite far from Bayonne.
The next town over, Jersey City, has a few very nice hotels harborside at Newport (about a 15 minute car ride from the entrance to the cruise terminal). On Hotels.com some that I have past by and they look quite nice are: Hyatt Regency on the Hudson, Doubletree Club Suites, Jersey City at Liberty Park, and lastly Courtyard by Marriott. The others that they have listed, other than the Candelwood Suites, which I know nothing about, are basically or at least appear from the outside to be, dives.I wouldn't chance it. These hotels are just across the river from Downtown Manhattan, so you might consider coming in a day or two early, if your schedules permit to enjoy a bit of what New York City has to offer, i.e. restuarant, shows, sight seeing. From the three hotels I mentioned you could walk to the PATH train and go one or two stops into Manhattan for a few hours should you so decide.
Good Luck,