Give someone back home the details of your trip, including a basic schedule and some contact information. Enroll in the U.S. State Department's Smart Traveler program and find out where the nearest embassy is at your destination. Make copies of your travel documents, including your passport and tickets, before you leave. Contact your local credit card companies to let them know you will be traveling abroad, as they can and will monitor your card and possibly cut it off if they detect any suspicious behavior.
Confirm your tickets and plan any transfers in advance so you don't get stuck somewhere alone waiting for a connection. Be prepared for possible snafus by keeping an eye on weather and political reports. Purchase travel insurance in case of cancellations. Hitchhiking is always dangerous, and if you decide to go camping, make sure it's in a secure site with good lighting.
Research that your hotel is equipped with adequate security and has a safe in the room or safety deposit boxes behind the desk. Keep the contact information for the local embassy on hand, and ensure your travel tickets and a copy of your passport are secure in your hotel room or safe. Credit cards and travelers checks, which can be canceled quickly, are always a preferable option in case you're concerned about hotel security. Bring your own rubber door stopper in case the lock on your hotel room door is unreliable.
Most hot spots in the Caribbean buzz with nightclubs, bars and dance festivals. This ensures a plethora of exciting, well lit and crowded areas that are relatively safe, but they present a number of dangers as well. If you're up for some nightlife, find a place to stay that's close to the action. Keep an eye on your drink, and never accept the gift of an open drink from anyone. Resist the urge for a midnight stroll on the beach, alone or not.