Unfortunately the bus network is not so well organized so a car is needed to visit the island.
If you come just for a couple of days, you can visit either Grande Terre : beach, countryside, nightlife or Basse Terre : trekking, volcano, wildlife.
Beautiful beachs : St Anne, Gosier, Malendure but best is Port Louis (I'm from there )
In Port Louis, there are less tourist but more mosquitos in the evening. You can swim or just enjoy a low deep bath.
Behind the cemetery, there is a protected natural site with mangrove, birds, etc..in one side and on the other one, beautiful small sany beachs.
At the entrance of the city, there is a sugar cane factory which has been transformed in a museum " Pays de la canne".
It's surrounded by cane fields where you can visit by a small toy train and it's quite interesting.