Use the ship or taxi excursions?
To rome in rome :)
Rome Italy is a long way from the port of Civitavecchia. A taxi would be over 100 Euro and take over an hour. You can take excursions from the ship or the train station is only a few blocks from the port. The train will take you into the main station in Rome where you can use the subway to get around if your comfortable traveling on your own in Italy.
When I have been in Rome it was the start and end point of cruises, not as a day port. I had my hotel arrange a car service to take me to the port or to drop me at the port. If I recall it was about 150 Euro for door to door. The drive took about 1.5 hour and the driver was moving fast, over 90 MPH when we got into the open highway in the countryside.
Just keep in mind, if a ship excursion is late, the ship will not leave you. If your on your own and your late, the ship may leave without you and your on your own to catch up with the ship.
Rome is a great city, I hope you enjoy it. One day is not enough to see everything in Rome.
That was a great answer, thanks for the info, i might share a taxi as there are four of us so might work out a bit cheaper.