They also have a very efficient public bus system in Grand Cayman. The fare is (if I remember correctly) 2.50 US$ per person per ride. The main bus depot is easy to find. Just walk straight into the town from the tender port area and then you see a square with the court house. The bus depot is on the other side of that square. You will recognize it because there are a lot of mini busses standing around.
We took the bus to Public Beach and just spent three blissful hours there bobbing around in the wonderful water with a view of the Disney Fantasy. We found everyone to be very helpful. The bus driver made sure to show us where to go from the bus stop (very easy to find, not difficult at all) and where to catch the bus for the way back.
Most affordable excursion ever for 5 $ each (in total, there and back)!