Calica has a beach resort very close, within walking distance, of the ship. I've forgotten the name of it. Ask a crew member and they will direct you. The Coba Mayan ruins are a fascinating tour if you are of that mind.
In Grand Cayman, I would suggest that you do the Stingray snorkle tour. It is wonderful and you get to swim with hundreds of stingrays. (What an experience for kids and you?)
Try to get on the first boat of the day. There will be a greater concentration of stingrays early in the day.