As south as it gets here

I dreamed a firefighter friend of mine who also was in my earliest band moved down to a remote beach town on a not particularly small island south of the Florida keys and north of Cuba. I had never heard of this island, but my friend explained that it was an anomaly: half of the island was considered in the state of Florida, but the southern portion was legally considered part of the state of New York, for some reason, and included three tropical beach towns (one called "Renton," for some reason). This gave rise to a weird trivia/joke about Florida's border with New York, and about gubernatorial voting trends. I described this to some journalist friends, who were as in the dark as me about this split-border island, and we resolved to travel down there to find out.