You could head downtown FLL or the beach at FLL. There is public transportation from FLL.
I assume you are going to use Tri-Rail which from the shuttle at FLL to the final station at MIA will take you about 45-55 minutes. There isn't really much between MIA and FLL. You could do a one day car rental (Hotwire or Priceline) to drive to downtown FLL or the beach. If you are talking this summer its going to be very hot & sweaty. On the other end, you could rent a car and head to Southbeach from MIA. Or maybe cab it to downtown Coral Gables for a meal-its about a 10 minute drive without traffic from MIA.