You don't have to go that far, take a trip to the canyons for some tuna fishing, plus you get a bonus of the bioluminescence when the water is disturbed.
I did a night kayaking outing in Fajardo, Puerto Rico a few years ago into a lagoon that was densely populated with bio-luminescent algae. As you paddled through the lagoon, you would leave a trail of sparkles through the water. You could grab the water and pour it through your hands and it looked a stream of sparkles. An awesome sight to see.
http://biobaypuertorico.com/
Puerto Rico is a beautiful and still wild place in extensive areas and going there was my compromise for my wife who wanted to go to "an island" in the Caribbean. I told her I wasn't leaving the US of A and going to a place where you have to stay on your hotel grounds or travel with guides and groups to preserve your safety. We rented a Jeep for the week and went anywhere we pleased without issue. The El Yunque National Forest, a true rain forest, was another highlight of that trip.
The best part was the local El WalMarto sold a stellar local rum known as Ron del Barralito. Hard but not impossible to find here.