You can get around the island by means of a taxi or a rental car. If you plan on staying just in Grand Case you really do not need a car almost everything is in walking distance or a taxi ride. If you plan on exploring on your own by the means of a rental car, it is suggested that you get a SUV rather than a standard Sedan. The roads in St Martin are very narrow and often include sharp turns and hills. Also keep in mind that there are hardly any signs in St Martin and if there are they are often hard to see. People will give you directions via landmarks rather than street signs since there are hardly any.
