Visa rules can be pretty tricky. What's more, they can change.
You must contact the Embassy (Consular Services) of each country on your sailing itinerary or the visa service of your choice for specific visa requirements, information, forms and fees for your nationality.
I recommend that you check your visa requirements with your travel agent or the appropriate embassy at least two months prior to travel.
Click here for a list individual country Visa requirements.
Visa requirements
Have a look at
Island-Hopping Experts who claim to be "the best Caribbean hopping experts".
Watch out for departure taxes as you go - some will charge you just for putting a foot down, others will let you off if you don't stay overnight, or if you leave within 24 hours.
Just make sure your papers are in order for each one, and you'll be fine.
Try using the "build your trip" flight comparsion tool here:
Flights to Caribbean
I hope this helps!