We didn't expect this port to be our favorite port in a Mediterranean cruise trip. It was beautiful! I read about the cable car and decided to take the local bus to go there. SO SO worth it! The ride was pleasant, the people in the bus even helped us by telling us where our stop was, they were so nice and happy to help, it left such a good impression on us. The ride to the top of the mountain is unbelievable, incredible sight. There's a small cafe & restaurant at the top where we had some coffee and a cappuccino. What an amazing experience. Then we went down to the old city to explore, with enough time to walk around, have some delicious gelato and see the Rector's Palace.
If you decide to visit the cable car (highly recommended) do that first or you may have to climb dozens of uneven steps to reach the street that leads to the cable car. Just take the bus right at the entrance to the cruise terminal (past the guard). Buy tickets at the small store near a bancomat (ATM) and wait for the bus to arrive. I don't remember how many stops there were but anywhere from 5 to 10. Either ask a local or just wait, you will see the cable car and people lining up on your right. To get into the city from there is fairly easy, just walk down the street and down the steps into the city. You can then leave at the end of the day through the front entrance. Remember to buy new tickets for the bus. I'm so glad we did it that way!