Salt Cay, Turks and Caicos.
Tiny island with residences around $175 per night with kitchenette.
Fantastic snorkeling, great diving (not Cayman great, but nowhere in the Caribbean is Cayman great).
Maybe 50 people living on the island.
Two bars.
2 miles of amazing beach where in my total 25 days on the island I have seen probably 15 people other than my wife.
From NYC there's direct flights to Providenciales (PLS) for around $450-600, plus you will need to add another $150-160 for the flight from Provo to Salt Cay.
I have no affiliation with the businesses there other than the fact we love them, we went twice in two years and we will be going again this year.
In February there's the migration of the humpback Whales and they can be seen all day.
Excluding diving, the cost is pretty low for the experience.
PM me if you want direct contacts.
Residence:
The very crowded beach