I'm trying to think back to when our kids were young.....they're all over 20 now....to answer your question.
Two out of four used to run high fevers when they got ear infections, which happened fairly frequently when they were under 2. It's hard to differentiate the early symptoms of an ear infection from meningitis in a child who can't speak....so having a hospital/clinic close was a comfort for us (I believe there is a vaccine for meningitis available now). One child was (still is) allergic to insect bites, so that was always a concern. The eldest son contracted 2 or 3 "weird" illnesses when he was under 3....nothing serious as it turned out, but nice to have good medical care close by. Our eldest daughter tended to get croupy which is scary but eased considerably with a vaporizer - doesn't work too well if the power goes out though. The cold, moist air of Vancouver also helped, so sometimes a quick trip from her dry room to the outside porch was enough to ease her symptoms. Our second daughter developed chronic bronchitis when she was around 1....we handled it with asthma medication and learned to listen to her chest to detect the possibility of pneumonia, which always meant a quick trip to the clinic/hospital/doctor. She "outgrew" the condition by the time she was 4.
I guess what I'm saying is it was always reassuring to have the clinic/hospital available when the kids were little....by the time they were in school (5 years old) we'd pretty much figured out what each was prone to and could deal with the cuts, scrapes, bruises and bleeding ourselves.
So thinking back, we would have probably been reluctant to take our kids to Roatan, until they were at least school age.