[Nyororin]

First, figure out why they want to go to the Caribbean. That may be a trip they`ve been looking forward to for years. If it`s been a dream of theirs for an eternity, and if you seemed to also be looking forward to it in the past - they may be hurt that you`ve suddenly decided you want to go somewhere else.
It may not have anything to do with thinking you`re crazy or with disliking Japan - I mean, just imagine if you had a trip to Japan planned and suddenly one person in your family decided they wanted to go to (insert random country) after you`d already made all the plans. I doubt you`d be too happy.

Give your parents credit - they have their own dreams and feelings. You may think Japan is "cooler", but they may not. There is no "right" answer to which country is better - it`s all opinion. No matter how you feel, they may feel the same way in regard to the Caribbean. How easy would it be to convince you that Japan wasn`t as good a trip as elsewhere?
You also have the entire rest of your life to visit anywhere you like - chances are, your parents work and can`t just drop everything to go wherever. Think of their feelings too.