Yes. I've used my VISA card in both of these ports.
I would suggest that you call your credit card company and let them know that you will be traveling to the Caribbean, so that they don't shut your card off. Some banks will do this as a "courtesy" if they detect an unusual spending pattern. I always call the week before I'm going and let them know where I'll be and for how long so that they can note it in the account record. I've never had a problem with this, but have heard horror stories from people who have. Apparently, it's quite a production to get your card re-activated from overseas.