We cruised out of Miami on the Magic last year and flew into FLL (because Southwest flies direct between Austin and FLL but not into Miami).
For a shuttle service, we used SAS last time and from the airport to Miami I was very pleased. Now, on the way back (port to back to FLL airport) I was not so pleased. The driver was totally insane. He was going 80 mph down the freeway (yes, I actually looked at the speedometer) and was weaving in and out of traffic, changing lanes and was generally aggressively driving. This all with toddlers in the van that were not in car seats. It was NOT OKAY.
So this time around for our upcoming cruise, I did further research and found that SAS, who is often recommended here on the DIS, is not well-liked on Yelp. However, I found two companies that have great reviews on Yelp and I will be contacting one of them for our upcoming voyage. I'm sorry I can't personally vouch for them, but here is the contact information if you want to look them up online or try one of them:
FG Car Services
www.fgcarservices.com
(includes car seats for free)
Jiffy Jeff
www.gojiffyjeff.com/
In terms of activities, I can't help you much with Miami. We just came in the day before and hung out in the downtown area in the afternoon/evening. There's a waterfront and mall we went to and a playground was near our hotel that my daughter enjoyed (we stayed at the Intercontinental).
We are cruising out of Miami again in March and again we're flying into FLL. This time we're staying the night in FLL in a hotel on the beach and we're going to hang out at the beach the afternoon/evening we get in and then take a shuttle to the port the next morning.