I have visited both Belize and Costa Rica, and it occurred to me in both cases that I wouldn't mind living there. In Costa Rica we had a tour guide who was born and raised in Iowa and had lived in Costa Rica for many years. However, he was not allowed to become a citizen, so every year he had to go visit somewhere else for a certain length of time (if I remember correctly, he would go to Chile.) To get a job without being a citizen, you must demonstrate there is no citizen who could do the same job. To become a citizen requires, basically, that you are independently wealthy.
This is just memories of a brief review of the requirements in place several years ago, but I think you'll find Costa Rica has the same general attitude about foreigners moving there at this time. I can't remember whether it was a similar situation in Belize, but I think so.