Depending on how many are traveling with you, I would say rent a car. We rented a car from Orlando airport to go to Cape Canavral port and dropped it off at the car rental located 1 mile from port. I don't remember if it was Avis or Hertz.
Or if you don't want to rent a car check out Tiffany Towncars or one of the other services. You can get a quote online. And it is definitely a hassle free way to go.