If you dock at Avinguda de les Andanes then you are almost very clost to the city center. You can easily walk there. If you dock more far away at Carrer de Botafoch it's approximately 1.5 km on foot. Walk along the marina in the direction of the upper old town, Dalt Vila.
TIP: If you want to explore the Old Town on foot, keep in mind the steep paths and streets. Wear comofortable shoes.