There is a good connection by public transport between the cruise port and the city center. Bus N°16 and 17 take you in a few minutes from the cruise terminal to Spilia, opposite the New Fort, just a few meters away from the historic center.
Bus N° 17 also makes a stop at the Old Fort. The fare is € 1.5 per person (one way). When you leave the cruise terminal, you can already see the bus stop at the parking lot, about 50 meters away.