"Grand Cayman has excellent health care and there are good clinics and facilities on Brac with access to higher level care on GC, but Brac may not be the best choice for an aging American couple. A big question is would we qualify for government-sponsored healthcare services because you don't pay any income tax in Cayman."
You cannot just move to The Cayman Islands and live here as a resident. You pay for a permit if you don’t have a job that pays it for you. As retirees you pay for the right to live here and you have prove that your income is enough for you to live and pay for any services you need including mandatory health care coverage as well as having invested required amounts in property and other obligations. Americans are required to pay income tax while they live in Cayman but it will be to Uncle Sam not The Cayman Islands. While it is true that we don't pay tax to the government here, we do pay hefty duty on everything. I consider "duty" another word for "tax" so in reality as Americans you will still be paying income tax and the hefty duty on everything you purchase which in part fulfills the government need to gather revenue from residents to cover the cost of services said government provides.