Your probably safer in those places than walking around any of the major US cities. There are places around Miami that are far worse. That said most of the precautions that work here are prudent there.

Don't flash money or expensive items. Remember that many of those island are poorer than most of the USA. An I-phone might not be anything special here but it might be considered special enough to draw unwanted attention there.

Try to blend with the natives. Jeans, or shorts, and a tee shirt are the uniform of choice in most locations.

Stay aware of your surroundings. Don't walk around with I-Pod earplugs in. Make eye contact and stay engaged. If something doesn't feel right leave. Don't drink, smoke, so much that your vulnerable. If you want to drink do it in areas with established security and people who are paid to take care of tourists.

An alternative to tourist areas is to establish friendships with the locals. This takes time, many trips and months, and effort but having a good friend in the local population is often better than all the high dollar security anyone could buy. Locals know what areas, and people, are safe to be around. They also know where the best food, drinks, entertainment, fishing, are. And are generally the best way to mesh with the local environment and authorities.