Going there in June for a week with the kids, and reserved a car through Thrifty - they are the only rental place that extends the rental to Nevis, so you can drop your car at the ferry on St. Kitts and they give you one on Nevis when you get off the ferry. Hertz has cheaper rates, but does not have the "Nevis perk". Having been bored out of our minds at Andaz Mayakoba without a car, it's definitely something that's a must for us. To echo 59Impala - As long as you can drive on the left (and possibly deal with a manual), it should give you the freedom to roam around the island(s), and not be a captive to Park Hyatt.

Not sure there's anything like this on St Kitts, but on Turks and Caicos, some rental agencies recommend to leave the car completely empty, unlocked, and windows rolled down any time you park to deter theft. No one is going to steal the car, but break-ins to steal things are supposedly common (not necessarily on St. Kitts though) - https://onemileatatime.com/keep-car-rental-unlocked/. Anyone have experience with this?