I used to rent a car and drove all around the island, circumnavigating it twice. Then I found us just driving around Negril and realized we were wasting money. If you're adventurous and want to explore the island, rent. I even downloaded a Jamaica map for my Garmin GPS. That would save you money vs booking tours. I've had some wonderful adventures driving in Jamaica. Those sugar cane trucks will play chicken with you though. However, it comes with all the responsibilities as noted previously.
An amusing issue is that the wiper and turn signal stalks are switched. You'll be wiping the windshield instead of signaling a turn until you've been there awhile. Then when you get home, you'll be retraining your brain all over again. Less amusing is making a turn and winding up in the wrong lane. I once turned off a roundabout in Kingston and wound up going the wrong way on a one way street at 5pm. Yikes! Same brain fart when you get back home. Drive safe! Respect --Marblehead
