Since your from the UK, any of the U.S. islands would be out due to Immigration problems. ( Your employable and have more than half a brain with the work ethic)
I assume its fixed wing? I suggest starting in the Bahamas and work down island. You can hop here and there cheap if you spend a few days and get to know some of the commuter folks. So I suggest starting in the Bahamas, Turks and Caicos, BVI, and as far down as Nevis if you have too. If nothing else you will have had a good time and see the places like few tourists do.
I have a few connects in a couple islands if you island hop and are living out of a back pack. PM and I will pass them on .
After having worked there for a few years Im jealous. It will be a fun experience even if you dont find work. Things are tourist price but you can do better.
P.S. Hope your single, you will understand once you get there.