We took the blue line boat service from Marco Polo Airport to the cruise terminal. This brings you next to the ship. During the 'ride' you get an excellent view of Venice, including San Marco. The ride goes very smooth. Costs: 14 euro pp single route. Even can be booked online in advance.
On our way back we took the people mover to Place Romale (1 euro pp) and then the bus to the airport (8 euro pp).
The ride by boat was the fastest (app. 1H).
You have to walk to the boats from the airport terminal with your luggage (7 minutes). But you don't have to hop over along the way.
From the cruise port to the old city center, its quite a walk. The route is ok, through shopping area mostly. It's worth it, because the old caravan serai is nice. We walked back along the sea. There was a nice walking path with a lawn.
An unexpected surprise! We tendered right into the little port of Dubrovnik and walked the tiny little streets and stairs of this nice old, but entirely renovated city. We had an ice cream and bought some souvenirs. The water is crystal clear at the harbour.