Jamacia-none-never get off the ship there any more. I'm afraid it's one of those ports we don't really like. Dunn River Falls is liked by some-climb a waterfall, and there is a river ride where you sit in an innertube and float down the river. Georgetown, everybody has to go to StingRay City once-swimming with the rays is amazing, and appears to be very safe. Cozumel, we like going to Canaanabe park(I know that's spelled wrong) It's the spot where you can swim with Dolphins (as an excursion-pricey tho), but they have a nice small beach, a pool with a bar in the middle, and plenty of space to watch the other people swim with the dolphins. Many times, for ME, the ship is the destination. We've cruised on Mariner 3 times before-it's a great size ship for ME-we also really like the Radience class ships.
Have a great time!!