It would be too much to hope that the proprietors have anything to do with the islands, or that they know the first thing about conch salad. The name, and the palm-tree poster in the front window, are more akin to wishful thinking shared with passers-by. ("Bahamas" plays well in winter; here's a name that makes a stronger appeal in the dog days of summer.)
This 24-hour market does stock several different hard ciders, including bottles from Spain and even Latvia, as well as dusty bottles of wine from California. Check that: "wine product."
Bahamas Deli Grocery
3317 Broadway (at LaSalle St.)
212-222-8001