Hi tarabert, Welcome to Cruise-Chat!
I hope you got my note about moving the topic here. On Grand Cayman - Stingray City is a must do! Cozumel is usually a beach and shopping day for me. Lots of good beaches there. Paradise Beach is a good choice, and Chankanaab National Park is great for all ages. You can take a taxi (pretty cheap) to either place. Less expensive to Chankanaab Park as it is closer to the pier. However there is an entrance fee, whereas Paradise is free, they do want you to order $10 per person worth of food/drink for use of the beach and facility. They are not real strict about this. I always do though, the nachos are awesome. They also have water toys for use for a fee. I'll post both links below.
I've only been to Roatan twice. Once I was rained out, and the other I did a privately arranged trip to a dive resort so I can't be of much help. I've heard Tabyana Beach is nice.
I haven't done any Belize excursions that I can recommend. I'm sure you'll get many more suggestions.