Best excursion in Cozumel, Grand Cayman, Jamaica & Gorda?

[MannieBothans]

We have never been on a cruise before, and we'd like to do something at each location that is unique to that location or best at that location. For example, is snorkeling for beginners better at Cozumel, Cayman, or Castaway Key, etc.?

 

We are doing a Disney Fantasy Cruise June 13th through 20th, 2015. We are a family of four, with a 13-yr-old son and an 8 yr-old daughter. None of us are dive certified and the kids aren't incredibly strong swimmers. We are more a fan of fish in the wild than dolphins in captivity. Our youngest is NOT a fan of stingrays, but our oldest is probably okay with them. Our son would like to see Mayan ruins, but I have not heard great things about the excursions in Cozumel, are there any better tours that leave from the port that tour the really large pyramids on the mainland?

 

The ship will be at Cozumel from 8:30 a.m. until 3:30 p.m.;

 

and then at Grand Cayman we tender in at 10:30 a.m. and tender out by 5:30 p.m.;

 

and then we will be at Falmouth, Jamaica we're there from 7:30 a.m. until 4:45 p.m.; and finally

 

at Disney's Castaway Cay from 8:30 a.m. until 4:45 p.m.

 

We are a fan of the cheaper things that might be found off the beaten path, but can pay for an experience that is really spectacular or one-of-a-kind. We are also more than happy to do something that doesn't take very long so we can enjoy the amenities onboard in a less crowded setting.