If you've got a bit more time to spend in exploring Miami, there's so much more than South Beach and even the cultural hotspots such as Little Havana or Wynwood.
There are state parks dotting the map, among those accessible from the area south of the cruise port is Bill Braggs Cape Florida and which features one of many lighthouses which can be found up and down Florida's coastlines.
I don't believe this one is open to the public when it comes to climbing!