Labadee is the private resort so you are limited to what RCI offers. There are several beaches, a zipline, jet skis. It is a nice stop.
Ocho Rios - don't go wandering off on your own if you've never been there. Stick with a ship's tour to Dunn's River Falls. Lots of beggars and panhandlers so you need to keep alert. There is a secure outdoor mall (Island Village) just a minute or two walk from the pier. It is a safe place and has a beach and a Margaritaville. Of course, it is also all commercial and not really Jamaica.
Georgetown - nice, clean, safe. A bit sterile actually but the Caymans are a very conservative place. You can safely book tours there with a private operator, although if you've never been there a ship's tour is probably wise. Stingray City snorkeling is the "premiere" tourist thing to do. You've never lived until a stingray glides over your body. There is also the turtle farm. It is interesting. Hell is pure tourist kitsch. All it is is a post office, t-shirt shop, and some rock formations (the hell part) in a swamp. The thing to do is send your family and friends postcards from Hell. It never made an impression on me and I never sent any mail from there.