Labadee is really beautiful and lots to do. They have really fixed up the port very nice and you can spend your whole time there if you choose to do so. Definitely at least allow an hour or two to walk around, see Dragon's Point and grab the lunch buffet (really delish jerk chicken!). We did the "island rum rendezvous" through RC and it was lovely. We boarded an open top boat that took us to 2 sandbars while providing beautiful views, lots of flowing rum punch, rafts and noodles at the stops. We did not want to go back! Great excursion. We had enough time to spend a couple hours on the port before leaving. Friends of ours did a snorkeling adventure where they were taken to 2 beaches. They really enjoyed this. Sorry I cannot remember the name of it. The 2 other couples in our group chose to hang out at the beach that day, one of the guys did the zip lining over the ocean and enjoyed it, but did say it was pretty expensive for how short it was.
Cozumel, there is so much to do. Our first time there we took a booze cruise, booked through Carnival, to Playa Del Carmen. It was a blast.. our first booze cruise and we loved every bit of it. Beautiful beach, free snorkeling, paddleboats, canoes, rock climbing wall blow up thing.. then it even had a pool and other water sports. We did the banana boat right off the beach and it was fun. The second time we were was with the group mentioned above.. we had a LONG time in Cozumel, 12 hours.. so we took our time getting off the ship after breakfast, then got in a cab and haggled for a deal to a good beach. Ended up paying around $15 a person, I think, to go to Planacar Place beach. Very nice, very quiet, free snorkeling gear. They also had some food there, drinks and even a place to get massages if you wanted. We just hung out while the guys did some snorkeling. Came back, headed back to the ship for lunch and to change, and then spent the rest of the afternoon doing tequlia shots, conga lines and dancing on the bar at Senor Frogs right in the port.
Never been to Falmouth, but if it's close enough to Ochos Rios.. definitely recommend doing Dunns River Falls. Wear good water shoes and bring a water camera.
Grand Cayman had a tropical depression storm while we were there, so we only got to see the shopping located right off the pier (this is a tendering stop). We wanted to check out the infamous beach, but the weather prevented it.
Have a great time!
Carnival Triumph - Spring Break Cruise - 2006
Carnival Victory - Birthday/Summer Cruise - 2007
Oasis of the Seas - Group Cruise - 2010