The old port of Santorini, named Mesa Gialos or Skala, is located below Fira. This is the port where the small boats transfer the passengers of the cruise ships and the boats to the volcanic islands of Palaia Kameni, Nea Kameni and hot springs depart.
There is a cable car that connects the old port to Fira town which is at an altitude of 220 meters.
The cable car of Santorini runs every 20 minutes all times of the year, except winter that it runs every 30 minutes. During the journey with the cable car, that lasts only 3 minutes, you can enjoy great views.
One way ticket costs €6 for adults and €3 for children. There is an additional charge of €3 for luggage.
For more information and detailed timetable you can visit the official website of Santorini cable car.
Other options to move from the old port to Fira town is to walk up about 600 steps or to ride a donkey or a mule.