Not much to do at Montego Bay, unless you take an organized shore excursion (I don't suggest Carnival's excursions) or want to spend a day at an all-inclusive resort..
As for Grand Cayman, depends on what you want to do. 7-Mile Beach is awesome if you want to spend a day at the beach. Sting Ray City is great for snorkeling with the sting rays. You can use public transportation to go to the beach, the turtle farm, or the little tourist trap call Hell. There is some good shopping, albeit expensive since it's a British commonwealth. And some great snorkeling.