We have stayed at both the Hyatt House and the Hyatt Place Fort Lauderdale Airport - South and Cruise Port. We gave the edge to Hyatt Place. They offer a free shuttle (that they share) from the airport to the hotel and a paid shuttle from the hotel to the cruise terminal. The first time we, we utilized the free airport shuttle - the second time, we just paid for an uber because we did not want to wait. We also used uber to get to the cruise terminal instead of the paid shuttle.
The hotels are across the street from each other in an area called Dania Pointe. Dania Pointe is like an outdoor mall area, so you have plenty of food options, a Sprouts grocery store and a movie theater within walking distance. There are also a bunch of other hotels in the area (we chose Hyatt because we had Hyatt points and it was free).
The airport, port and hotels are very close. The hotels cater to cruise guests with almost all the big hotels offering paid shuttles to the cruise terminal (a lot of them are large vans with a trailer attached to haul luggage). We also had no trouble getting Ubers - they do a brisk business when cruise ships are in port.