They all have their own perks.
Been to the Bahamas a few times and its very touristy and we got bored with it after the second time. Grand Cayman was really pretty and it was a cloudy day. Our ship was detoured away from the Western Caribbean which we were looking forward too but we ended up in Ocho Rios and the Bahamas again. We were part of a 'tour' but we still didnt feel safe in Jamaica. I mean there was a huge gate between the pier and everywhere else, they asked for ID to go thru the gates too! Even the parks we hit had huge gates. We walked Dunn rivers falls which was amazing and our legs hurt for days after that but upon return to the ship we were 'convinced' to purchase these nicknacks for $20 and we gave it to him so he would go away. Then the rest of them flocked towards us for money. It wasnt till after that the tour guide told us to stay away from these people. $20 is well over $1500 of their currency. Be careful on ANY island and stay with your groups.
On the travel agent side - if you book out of any florida ports the cruise will cost a lot less then say NY. There is Port canaveral in central florida and there is port in Miami and Ft Lauderdale. Check all the cruise lines to see where they go, the longer the cruise the more ports it may have. I try to take cruises that have many ports since I dont want to be 'out to sea' for too long. I dont gamble and I dont drink so Im afraid I would get board really fast. lol. They do have activities, parties, games you name it. I once took our kids on a cruise to no where! Those are good starter cruises. Even a 4 day cruise is a good starter cruise. I tell everyone to try a shorter cruise before taking a longer one just in case.
They have cruises that go from florida to california thru the Panama canal - I would love to try that!
There are so many cruise lines to choose from, good luck!