We hired a car on Grand Cayman and drove to Rum Point which we thought was really great. We hired the car through Avis. When you get to Grand Cayman, you go to the Blue Iguana shop and then a car comes to take you to the rental place which is at the airport. You return the car to the airport and are then driven back to the dock. The Blue Iguana is about 2 minutes walk from the dock.
Rum Point was great, with snorkelling, swimming, and I think some other water things which we didn't do. you can get food and drink there (but beware, prices are in Grand Cayman dollars which looks cheap but when the bill comes the US dollar cost is higher).
By having the car we were able to leave the beach when we wanted and had time for a drive round some of the rest of the island. We also got there well before the excursion did which meant we (a) had the pick of the seating and (b) the best of the beach before it got busy.