I was exactly in your position 7 years ago. I did a lot of research on web sites like this one. Especially the chats regarding ports of call. First, make a list of what everyone likes to do. Shop, snorkel,golf,beach stuff,hiking, biking, etc.... Also find out about sleeping habits. Do some like to sleep late, early risers etc.. Then, decide on which ports give you the best chance of finding what you like to do. You also need to look at how long each port visit is so that you can decide if there is enough time to get your activity in. Also, check out private tour companies and not just the ship excursions. Usually, you can get off the ship, find your tour, and be off quickly before the large crowds of ship sponsored excursions even get organized.
I've been on the Liberty (great ship !) also have been on two other Carnival ships.
I have been to Cozumel, Grand Cayman, Jamaica, St Martin, St Thomas, Bahamas if you stop in any of these ports, I can help you find the best places to go and good tour companies.