NCL has a number of Bahamas cruises out of NYC on the Jewel and the Gem. Two nice ships.
NCL is Freestyle and will give you many options in dining times and venues plus an easier disembarkation and some great entertainment options.
With NCL there are a number of additional charge restaurants but plenty of included restaurants. If you add $100 to your cruise budget you will have a great time. NCL is usually a little lower in fares and even with the additional $100 it will be equal to many other lines.