Public bus from Genoa to Genoa (city)
From the Marittima / Principle F.S. bus stop you can take bus N°32, 9 or 11. They stop at Piazza Caricamento opposite the Old Port near the center of the city. The buses run every 5-10 minutes. It's only 2 stops and you pay € 1 per person (one way).
TIP: You can find the bus stop after 20 meters on your right when you walk from the cruise terminal to the city center.