The name of the marina in Islamorada at Founder's Park is Plantation Yacht Harbor. As mentioned, great place for the family and central Keys location. I don't know what you gain going to Miami and Key Biscayne that you can't already access by car from Ft. Lauderdale. On your way down to the Keys, anchoring in, or outside of No Name Harbor is a highly recommended experience. Good dinghy exploration available from there plus Billy Baggs state park and good Caribbean food at the Boaters Grill in the harbor. You can dinghy through Stiltsville or meander through there in the big boat on your way south/west.
Thence to Eliott Key anchorage, take the dinghy to Eliott Key (there is a small boat "marina" there for good hiking and exploration. Also dinghy to Boca Chita, worth seeing, and if not the weekend you could dare to take the big boat to Boca Chita and tie up in the basin. Not our bag but we always enjoyed an hour or so at Boca Chita itself.
Thence to Pumpkin Key to anchor out and take the dinghy to explore Ocean Reef club and environs. Here is your last chance for awhile to go outside via Angelfish Creek. If you head inside, Tarpon Basin presents another good anchorage with land access.
The ICW starts getting a little skinny for deeper draft boats, after Islamorada though we did it all the way to Marathon once, sanding the bottom 3 or 4 inches of our 5 ft deep keel a bit. If inside and not staying at Plantation/Islamorada or taking a transient slip there, anchor out in the bight and dinghy to Lorelis and or World Wide Sportsman and hang out, eat, drink. Shell Key and Lingnum Vitae Key are fun state park explorations as well, I think they still have free moorings off them but haven't been by that way in a few years. You can then go out Channel 5 to avoid the skinny water.
We loved staying in the mooring field at Marathon, did so for a couple months one year and a few weeks another. We like the community, and dinghying to the beach and around the area. If you don't have a car (we did shuttle one of our cars down there), you can take a nice cheap bus to Key West which I far preferred to taking the boat there; we'd anchor off Fleming Key when we did. We also enjoyed the week or so we spent at Marathon Marina which has a good cruiser community as well. Using Marathon as a base, we'd occasionally take the big boat to anchor in Bahia Honda, another fun spot to explore via dinghy ( make an adventure to Big Pine/No Name key and the perfunctory lunch at No Name tavern for good pizza)with the best beach in the Keys.
A lot more, but that's a capsule.
