It seems that NCL does offer a few different tour options in Miami - the kicker is they appear to be only on the longer sailings, where Miami is a port in the middle of the cruise, rather than the final debarkation city.
Heck, I don't mind paying a fee to store my bags so I can explore Miami without having to haul them around all day. I was even considering renting a motel room to keep them in for the day - then realized most motels don't start their check ins until well after debarkation time from the ship. Silly me!
We are hoping to stop in and see the aquarium we missed last time.
The airport website you posted seems to have a program, like mentioned, so I think I will look into that. It even has a map of the airport on there too. I have been to Miami once in the past, but was on the Greyhound that trip, so a map will come in handy as well.