Cruises just aren't for me, but you may be different. I don't like them because you spend a lot of time on the ship and don't really get to experience the places you visit for very long.
Most itineraries have you spending anywhere from a few hours to almost a day at any one port. The ship generally gets into port in the am and then a whole mass of passengers engulf the island. Places close to the dock get swamped with people, so if you want to avoid the crowds (and get away from the worst of the touristy chintz that's sold) get as far from the dock as possible.
As far as good cruise lines, I've been on Norwegian and they seemed to be very good. My family is very cruise oriented and among my cousins, aunts, uncles, sisters, mother, etc they've hit all the lines. They say Carnival is ok but quality is a little worse than the others. Disney is supposed to be really good (but you've already nixed that). Princess is another they really like and Holland America they said was very nice.
One tip I can give is to try to plan your own excursions. The cruise's trips are overpriced and generally not with the best providers on the island. Making plans on your own will save you money and give you better experiences than the typical cruise alternatives. To do it, check out the island's websites or go to this site (sorry to the TFP for pointing to another site but this place is a great resource for those interested in cruises)
http://cruise-forums.com/forums/list.php?f=67
Daytime activities on the cruise I went on were limited. Hanging out by the pool was the biggest daytime past time and getting lounge chairs could be dicey (so get up early and snag a couple). Night time was great, comedy/dance/other shows to pick from, karaoke, clubs, the casino, etc.
Hope you have fun and good luck with the arrangements!