Frankie's Pizza, Best in the World
If you like pizza, you need to head a few miles south from the airport to
Frankie's Pizza, 9118 SW 40th St (Bird Road), (305) 221-0221. It's take out only, Sicilian style.
Frankie's Pizza has been around for over 50 years. It's still run by Frankie's family. You can watch them prepare your pizza. The ingredients are superb and the final result is even better.
http://www.frankiespizzaonline.com
My mouth is watering, just thinking about it.
As for other suggestions, tell us what your interests are. I'm a Miami native and at least a 5th generation (really) Floridian, although I'm currently in exile.