Are you talking about taking a cruise, or moving to a new country? You can't just move without having a valid visa, you know. Many places south of the US are not islands- Mexico, Central America, northern South America. Islands can be expensive because things have to be brought in by ship. The Grand Caymans are the most affluent of the islands, with jobs available in the financial sector. It's relatively easy to immigrate legally to Mexico, Costa Rica or other Central American countries. But you really need to be clearer about what you want.
Cruises typically visit several islands, and sometimes visit Central America.