No need to re-post -- I just moved the thread to our Europe section.
Martine, take a look at some of the threads in the Europe section, particularly the one on train travel in Europe. We took a ship's excursion to Rome when we docked in Civitavecchia last year, yet that is not your only option. Yet, we felt it was worth it for a first-time visit. It was a full-day walking tour that visited the Pantheon, Piazza Navona, and St. Peter's Square, among other sites.
I haven't been to the other ports, although we did spend a short amount of time in Nice. We had docked in Monaco and took an all-day tour (offered through the cruise line) that covered Nice, Eze, and Monaco that was very nice.