I enjoyed driving the north side of the island. There was a trail that ran down the coast from the lighthouse to some ruins. Our rental car was a beat up jeep wrangler though. We didn't see any people until we reached the ruins.
Definitely rent a jeep for a day or two. We went back in 2010 or 2011 and that was probably our favorite part. You can hit up a bunch of different beaches, ruins, off-road trails, natural bridges, etc. Always felt safe too.
Driving the island is a must. We had more fun climbing/exploring than we did on the beach. Look out for snakes though. We saw a TON on top of the iguanas and other wildlife.