There's a couple different hotels near the area, that I haven't stayed at, but have had success with the brands in the past.
The first one is the Comfort Inn Airport / Cruise Port South
. This hotel looks like they have a shuttle service to and from Port Everglades, as well as the airport. Not sure if it's continuous, or if you have to call ahead to reserve it.
The second one is the Comfort Suites Airport and Cruise Port
. This would be nicer than the other one, as the rooms are mini suites, and the other hotel would just be standard rooms. This hotel has a park and cruise package, however, they don't mention anything about a shuttle to the port in the hotel description.
Whenever I travel, I always try to find Comfort Inns or Comfort Suites, and have yet to be disappointed.