We visited Grand Cayman a couple years ago. There were a wide variety of great shore excursions to choose from. We chose the Stingray Sandbar, Hell & Turtle Farm Experience. I would happily do the same excursion again on our next visit.

Here are the ones listed in the Carnival shore excursions book. Not all excursions will be available for every cruise, or during every time of year. Other cruise lines probably offer the same or similar excursions.
Excursions can either be booked through the cruise lines ahead of time, or while on ship. Booking the excursions directly with the operators is also an option. This can save you money, but involves risk if there is a problem.

Aqua Boat & Snorkel Adventure (3 hours)
Atlantis Deep Explorer (1.75 hours)
Submarine dive to a depth of 800 feet.
Atlantis Submarine (1.5 hours)
Explore underwater park in submarine at 100 feet deep.
Beginner’s Scuba Diving (3 hours)
Butterfly Farm & Beach Adventure (3 hours)
Cayman 7 Mile Beach Break
A day at the beach.
Certified Two Tank Dive (4 hours)
Coral Reef & Stingray Safari (3 hours)
Fisherman’s Rock Swim & Snorkel Adventure (2-2.5 hours)
Grand Cayman Highlight Tour (2 hours)
Grand Cayman Island Tour (2 hours)
Crand Cayman Kayak Safari (3 hours)
Grand Cayman Snorkel Tour (2 hours)
Reef & Wreck Snorkel Tour (2 hours)
Sail, Snorkel & Stingray City (2.5 hours)
See & Sea Island Tour (3 hours)
Shore Snorkel Experience (2 hours)
Snuba (1.75 hours)
Snuba combines snorkling and scuba to allow diving deeper than snorkle without tanks.
Stingray City & Island Tour (4.5 hours)
Stingray City Tour (2.5 hours)
Swim with stingrays!
Stingray Sandbar Tour (2.5 hours)
Swim with stingrays!
Stingray Sandbar, Hell & Turtle Farm Experience (4.5 hours)
The Trolley Roger (1 hours)
The Ultimate Undersea Adventure (1 hours)
Explore the marine life in a semi-submarine.
Brittania Golf Club