We will be on a cruise the last week in May 2014.  One stop is George Town.  Wondering what you recommend for a couple in their 70's who are not likely to swim with the rays.  Is there a tram that will show us around town with a stop for some of the popular Rum Cakes?  Any suggestions for how to spend the day without getting into swimwear.  Interested to see the 5 mile beach and perhaps enjoy a chair in the shade with a cold (non-alcoholic) drink.  

You can do 5 Mile Beach. You might also enjoy visiting the turtle farm there, which is actually a "farm" for the preservation of sea turtles (not for eating them). They have an interesting program. Best thing to do would be to share a taxi with some of your fellow cruisers.

Ye there are definitely a bunch of thing. 

7 Mile Beach is certainly great, and tons of little shoping and things to do from there - http://www.caymanislands.ky/activities/beaches/sevenmilebeach.aspx

Turtle Farm - http://www.caymanislands.ky/activities/attractions/caymanturtlefarm.aspx

Queen Elizabath Botanic Park - http://www.caymanislands.ky/activities/attractions/botanicpark.aspx

Thank you for your suggestions.  We did enjoy 7 mile beach and the beautiful white sand.  The weather was perfect for lounging on a rented deck chair and an umbrella shading us from the tropic sun.  Took lots of pictures of the beautiful water and our adult kids playing in the sea.