Shuttle bus from Valencia to Valencia (city)
Given the large distance between the port and the city center, most cruise lines provide a shuttle bus (whether or not complimentary). Most buses go to Plaça De L'Ayuntamient, right in the center of the historic city. From there you can explore everything on foot. Better check the price (if any) in advance. The public bus costs only € 1.50 per person (one way).
TIP: At the information desk of the Tourist Office in the cruise terminal you can buy a Valencia Cruise Card (VCC) for € 10 per person.This includes a shuttle service, information about the city and some coupons.