In the US a very high percentage off the medical costs are regulatory and liability insurance related (maybe 70%). There are also new treatments that take many years to get approved in the US. That delay literally costs many people their lives every year. So there seems to be a business opportunity to do things both better and cheaper. Some possibilities are listed below.
Some small islands, like Anguilla, have medical centers that do plastic surgery mostly for tourists. It seems people like to be away while they have their surgery and while they are recovering from it. Then when they come back and look different they can tell people that their vacation did them good.
There are also cancer treatments, like mono-clonal antibodies that seem interesting. One way to do this is to clone antibodies from the patient that target their cancer cells, put radioactive material into these cloned antibodies, and put them back into the patient. The radioactive material has a short half-life, like a few days. The antibodies find there way to the cancer so that when the radioactive particles come out they do a good job of taking out the cancer with minimal collateral damage, compared to other treatments. It seems to work rather well but it is not like the normal pills that the FDA is used to licensing. The tag line is, "giving your antibodies nuclear weapons so they can fight your cancer better". It has been around for 20 years and yet probably won't be permitted anytime soon in the USA. It seems it is not that hard to do (I knew someone who learned how to do it and did it as a summer student one summer).
Other possible treatments could be emerging new chemotherapy agents that are still working on their FDA approval.
There may be possibilities with stem cells. Things are changing fast.
Gene therapy is another cutting edge medical technology where regulatory approval is slowing things down.
Even plain old regular healthcare made more affordable would be a huge benefit to many people.
It would be very "politically incorrect" for someone's navy to sink a hospital and kill all the doctors. Even just shutting it down without sinking would probably be viewed as wrong. This is in contrast to something like a drug resort where nobody would seriously complain when the US seized the thing.
If this were on a migration route there could well be a set of countries that counted on this for some medical services.
There has been discussion of this topic in the forum.