It is easy to walk from the cruise port to the city center. It will take 15 to 20 minutes. The first part is less interesting as you walk through an industrial part of the harbor, but once you arrive at Porto Antico (Old Port) you get a taste of what the city has to offer.
Take the stairs up near the cruise terminal. From the square with the fountain, cross the bridge and turn right. Follow the main road along the viaduct above you. Soon you'll reach the Old Port. There is also an information kiosk of the Tourist Office. Opposite the Old Port begins the historic center.