I just did a Miami (well, Sunny Isles) trip with a preschooler and a just-barely toddler, and it was great from a beach perspective but it wasn't that great in terms of accessibility to other attractions. Distances to downtown areas in FLL/MIA were fairly significant and when you're dealing with young kids, a 45 minute highway drive each way really cuts into how much you can do in a day. We had fun in Sunny Isles but we ended up scrapping some attractions we were originally planning on visiting, like the zoo, seaquarium, etc.
We'd like to go back in a couple years and tack on a few days in MIA after a cruise... when we do that we'll definitely be staying in or around downtown Miami and make those kinds of attractions more accessible.