Good advice here. However, though visiting the Florida Keys may be allowed by the aircraft owners, I would not insist on leaving United States territory; there are a lot of illegal drugs that travel these routes, so big problems could result. If I were you I would rent the plane for a week, and go up the west side of Florida, the panhandle, and New Orleans. Then back to Alabama, Jacksonville, and down the Atlantic coast. All nice warm water, most of the year. And stop by at Jack Brown's seaplane base, get your float plane rating!
Have fun!