I would not recommend renting a car unless you are good at driving in other countries - they drive on the opposite side of road and have roundabouts.
I would hire a driver - it is cheaper than renting a car for a day and risking an accident!
Also, hit the grocery store at the roundabout. You can make breakfasts in your room, sandwiches for lunch. You will save a ton not eating out 3x, plus Red Stripe and rum is cheaper in your room as well. We still go out a lot, but usually have a few before we do.
You will be in heaven. Do not do an AI. For the extra cost of an AI, you can eat/drink like a king in Negril!