I use my credit card in Jamaica all the time, everywhere, without issues. If there were an issue, my liability is $0. My card charges no transaction fees at all, so I get an excellent rate.

I wouldn't use my debit card as a credit card there though, only to get cash from an ATM. I don't want to have $ taken out of my account while they sort out any fraud. So I only use the actual credit card for purchases there.