The port for Rome is about an hour or so from the city. Take the train to Rome as it is much quicker than an excursion bus. The train station is a short walk from the port entrance. The round trip is 9 Euros and also includes use of the metro in Rome. Rome can easily be walked if you have a good map.
Stay near the water front. You can then take the metro into the main city if you wish. The aquarium was a must see. It is located near the cruse ship terminal. Be aware that there are some teenagers that may try to pick your pockets. Be safe and keep your eyes open for this.