i cant help you out on the gran cayman islands, but Cozumel mexico is awesome..i would recommend going snorkeling.. its a great way to spend the day...when i went on my carnival cruise i wasn't sure what to expect...but it was the best vacation ive ever taken! don't forget the sunscreen..even if you don't get burnt in some place like florida...the sun is so much different on a cruise in the Caribbean. trust me i learned the hard way... i was so burnt that the bridge of my nose was swollen and i could see it ( not normal for me) lol