I agree with JusMe about staying in Rome. It is a long way from the airport to Rome and also quite a ways to the port from Rome. We have been in and out of Rome a lot on cruise ships, one time even on a European coach tour. I didn't see much around the port that would be of interest even if there is a decent hotel. It would be a shame to stay that far away from historical Rome.
As far as we are concerned, we always book the cruise line airport/hotel/port transfer packages. One time Air Alitalia lost every single one of our bags (we were first class too), we arrived shortly after noon the day before embarkation on a 5 week cruise, which didn't take place until 6:00 PM the following day. It certainly was calming to have a cruise line contract rep meet us that time with a sign and our names. The rep was able to handle and speak the language of Air Alitalia personnel, who have to be among the worst in the world, and fight our lost baggage situation for us with them. The rep was there for us as we had paid for his services, other irate and frustrated cruise line passengers had also lost their bags, but they were independents who preferred to do the transportation and hotel arrangements on their own. They were pretty demanding, I will say this for the rep, he did his best to try and help them out for free.
As it turned out, our bags showed up 20 minutes before they pulled the gangway. We had given up. We would have never gotten our luggage, if it wasn't for the persistent efforts on the part of the cruise line, Regent.