At least some of the islands have rules that require locals be hired unless the job requires skills that can't be met by local hire, so part time or short term work will be more difficult or impossible to find on those islands. Jobs filled by outsiders are usually professional - Doctors, scientists, etc. You will need to look into that.

Let me add further to what Sassafrass wrote.

You CANNOT just show up on most islands one day and expect to work. Almost every Caribbean islands, including all those in your tag, WILL NOT allow anyone who is not a citizen of that particular island to work on the island without obtaining a Work Permit and these are often very difficult to get. You have to possess a "unique skill" and your potential employer must prove that there are no locals on that island qualified to fill the position. Assuming you have such a "unique skill" you would then have to apply for the permit which may or may not be approved. If approved you'll have to pay the required annual fee (anywhere from $1,000 to $5,000 depending on the island). You should know that, depending on the island, the application process can anywhere from 3 to 6 months and there's never any guarantees the Work Permit will be granted.

What this all means is it is doubtful anyone just graduating from college would be skilled enough to be granted a Work Permit and even if they did have the necessary qualifications to fill a particular position it is doubtful any potential employer would be willing to go through the process for a part-time worker or for anyone who would only be on the island for 6 months.

Now, if you are a US citizen you would already have citizenship and work status in Puerto Rico, Vieques, Culebra and the US Virgin Islands so it will be infinitely easier for you to live/work on those islands. Likewise, if you are a citizen of an EU Country you could live/work on St. Martin or one of the other French islands.

If you are a US citizen and want to pursue your dream you might want to visit the Virgin Islands Moving Center website (www.vimovingcenter.com). It's a website dedicated to living and working in the US Virgin Islands. There's a ton of information there including a very active forum. Read all the material there (it will take you weeks there's so much info) and look through the thousands of posts in the forum archives - you'll find answers to every question you have and hundreds more you haven't even thought of yet.

And to add more, living expensive are huge in Caribbean, expect at least 3 times than the states. Rent will run you about $1500 for a small off the beaten path place. Cars will cost you 3 times more, but you'll need transportation. Utilities, expect $300 water bills, $600 electric. Food, gallon of milk $10, bread $6, beer $60 a case. So even someone who has saved quite a bit, won't last long.

Be smart. Travel if you can. But save your money to start up wherever you're going to live when you return, you're going to need it!