One summer 7 or 8 years ago I went to the Dominican Republic, decided to go deep sea fishing, I add I'm not a fisherman,but thought it would be an interesting day out..........wrong we chugged up and down what ever sea it was for 5 hours not a damn thing , the other boats also filled with dollar rich tourists
had the same experience, it was only when we returned to port and was departing an experienced crew member recommended we come anytime between January and March when you can catch good big fish !! , finally you mention Cuba, I was there in April this year, didn't go fishing but spoke to lots of people who did and they were really pleased, I would recommend a day or two in Havana, fasinating place,stunning arcitetcure( can't spell) great experience, go now if possible because when fidel goes it will all change and it will just be another tourist destination.........good luck