There’s no single version of the Caribbean. Sure, the water is blue—sometimes turquoise, sometimes electric teal—but the similarities start to splinter from there. Some islands are lush and volcanic, with rainforests spilling into the sea; others are dry and desertlike, dotted with cactus and wind-bent divi-divi trees. In St. Barts, you might hear French and smell fresh-baked baguettes. In Dominic...