SunBeach has a large parking area. I would say if you're going anywhere in that area just park at SunBeach. Just please please have some lunch or a beer at SunBeach. Don't just use the parking lot, lounge chairs and umbrellas and not have the decency to buy anything (like some people do). I'd say if you're just using the parking lot, grab a beer to go and walk the beach. Margaritaville has a large parking area as do just about every venue on the beach and in the cliffs. LTU parking is across the road.

I think parking is the least of your worries tropicdaze. Pot holes, crazy drivers, goats on the road, that's what I would be concerned about.
(I love driving in Jamaica BTW)