You know, I just assumed tropical from the question, but I think Iceland would totally count as a beautiful island. As would Ireland. I'd happily go to either.3, no doubt!
I hope I'd be allowed to pick which island, I'd love one in a colder climate with plenty of snow. Or at least one that isn't too tropical with plenty of trees for the cats to climb and places to explore for them
Maybe it could be one of those cat islands off the coast of Japan? They usually have a small fishing village on them, so plenty of cats that need to be TNR'd, kittens that need new homes, shelters and feeding stations that need to be built. You'd achieve a lot in a year.3 Cats aren't going to rescue themselves, why would I want to be stuck on some island?