Hotel shuttle vs. taxi to Port Everglades

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We will be checking in to our hotel ( either LaQuinta in Hollywood, Sleep in Dania, or Hampton Inn in Plantation) around 10 or 11 p.m. on a Wed. night for a Thursday morning cruise departure. As I understand it, you need to sign up for the following days shuttle to the port. We like to arrive at the port as early as possible. Do you think all the early shuttles with be spoken for by then? Could I have them call a cab and if so what would be an estimate of price from the above mentioned areas to the port?

 

Thanks!