Are caribbean schools good or bad compared to american schools?
In general, you want to go to a US MD (and in my opinion DO) school over a Carib school.
There are a number of additional hurdles Foreign Medical Graduates (including Carib grads) must contend with that US Grads do not face. While the entry standards are traditionally lower to Carib schools, there is significantly higher attrition, meaning a class of hundreds may begin but half or fewer than that may actually graduate. Despite this, everyone is still charged the (high) tuition which is difficult to pay-off if you do not wind up with an MD behind your name. The graduation rate in US schools is roughly 95% and a significant number of those that leave are for non-academic reasons.
Carib students also have the issue of rotations. During year's 3 and 4 of medical school most US MD students are able to do their clinical rotations at affiliated hospitals and places locally.
When it comes time to the Residency match, do Carib grads get good residencies? Yes, it does happen. You can always find a story about someone from X carib school who made their way up to a great prestigious spot. This is a notable minority. US Allo grads will have the first draw for most residencies.
Would it be better to goto a college like NYU and then re apply to med school, or goto a caribbean school?
I'm not sure what you mean by re-applying to med school? I'm assuming you're a HS student, possibly having applied to a combined program?
I would absolutely recommend you attend a 4 year college (doesn't have to be NYU, but that wouldn't be a bad one) and then apply to US allo medical schools via the standard track.
I'm going to recommend you not apply to Carib schools until you've exhausted your options within the US. It takes many students multiple cycles of application to be accepted, but this (again in my opinion) is still a better option than rushing straight to a back up plan.
And what colleges/universities are great to goto in the caribbean?
If absolutely everything else has failed and you're going to apply to schools in the Carib. My understanding is that St. Georges University and Ross are the 2 medical schools that are worth applying to. Everything else get's more sketchy and less reputable when you're trying to match.