This port is called Civitavecchia. The harbour provides free shuttle buses to the city. From the bus stop you can walk in 15 minutes to the train station where you can get on a cheap train to Rome for 7 euros in 70 minutes or you can take a quicker and expensive train.
We were in Palermo on a sunday afternoon. Museums that should be opened, were closed and most shops were closed too. Taxi's are rather expensive. The city is poor and rather filthy
In the port of Palma de mallorca, there is no sufficient public transport, but there are a lot of cheap taxis. We took a taxi to Palma Nova to go to the beach.
Awfull. The ship docks very far from the city. The taxis are extremely expensive. The shuttle bus was 7 euros per person and took 30 minutes and 20 minutes waiting time to get to the uninteresting city. Stay on the boat!