From GoToCayman.com - the Wiki for Cayman
Remember that they drive on the left in Cayman! Seat belts must be worn by the driver and all passengers. Visitors must buy a temporary Cayman driving licence (for each driver) from the Police Station or Rental Agency Desk at CI$5.00. You have to be over 21 to rent a car in Cayman, but some agencies won't insure renters under 25.
Traffic to/from George Town can be very heavy in the morning and evening rush hours.
Whether you need a car for your whole trip will very much depend on where you are staying; if based in the Seven Mile Beach area you may want a car for a day or two to explore other parts of the island, but if you are staying somewhere remote (North Side), then you'll need a car to do your shopping etc.
There are a wide range of cars available, and they can be in a range of combinations of left/right hand drive and automatic/manual (shift stick). If you have a preference check with the rental agency in advance and make it clear what combination you require. There have been occasions reported when there are no rental cars available at any agency (this is especially true in peak season), so at these times it is probably best to book in advance. Having said that, there have been a number of reports on the various message board where visitors have got a walk-in rate better than anything advertised. If you are prepared to be flexible and don't need a vehicle for your whole trip, this may be the best option.
Some visitors believe that if they book the car hire on their credit card it gives them the legal and insurance protection they need; please check the conditions of use of your credit card carefully as often these perks only apply when hiring a vehicle in your home country and not when you are abroad on holiday.