We've been on all these cruise lines and have sailed out of NY on several occasions. The one thing we've learned in our 46 cruises on 11 cruise lines is that there is something out there for everyone, but what one person loves, another will hate. You'll get as many answers to your question as there are people because everyone is different and what they think is the best, you may not like and vice versa. Not only is each cruise line different, but each ship within that same cruise line can be different. And even each ship can be different at different times because they go through refurbishment and crew changes. Some people love big ships, while others prefer smaller ones. Some like the old-school style, while some like the more modern designs.
And as we all know, food is very subjective! Some people will swear the food on one cruise line is outstanding while others will say it's the worst food on the high seas.
Opinions are like bellybuttons and everyone has one!
With all that said, it really depends on what you're looking for in a cruise, your lifestyle, and your budget. And that's the fun thing about cruising is trying them all until you find what's best for you.
Personally, I'd like to try the new NCL Breakaway for the newness of the ship, but we prefer Celebrity for the food. RCCL has alot of amenities and Carnival attracts a younger crowd. Princess, in my opinion, is better than RCCL & Carnival, but I know others will disagree.
As for beaches, NY is quite a distance from the Caribbean and results in a longer cruise, so if you want to go there, it would be better to sail out of Florida.
Lots of options.