If renting a car (and you'll miss a lot if you don't), just don't be afraid to 'off-road' a bit. This is how you find hidden beaches and super picture places. You can always ask directions and the island is small so you can not really get lost. All roads are either a dead end or lead back to the main road.
We had such a great time at the local festival we dropped by. It was "field day" sorta thing going on. Yummy grilled chicken, friendly people and a break from being at the beautiful beaches. The girl that was traveling with us also made a friend for the trip and a penpal!