The problem with Civi. (for Rome) is the early departure time. I always like to try to do my own thing when on a cruise. A 6.45am arrival time will probably translate into a 7.30am time off the ship. If you hoof it you might make a train at 8amish. That is about 9am arrival time into Rome. Going by road (some type of transfer or tour bus) won't be any faster.
For a 5pm departure time 'all aboard' will be around 4pm, which translates into leaving Rome at around 2pm, or very soon after.
Depending on their times you may be able to beat the clock a little bit by using the long distance non stop trains to Rome in one or both directions- they take 35 minutes or so.
All that means that the ship's own excursions are going to be a bit rushed as well.
Faced with exactly that conundrum, and my propensity to wander on the way to the station, I opted for a relaxed self guided walking tour of Civi (with a map acquired at the Tourist Info ship side)- but you should also be able to pre book a similar thing as a guided tour. Or the Taurine Baths, a few miles away by citybus (or probably on a guided tour) are supposed to be rather interesting. Civi is an old holiday resort for Rome (as well as a port), has Roman ruins to explore (including within the dock complex), a couple of nice Churches and shaded squares to be, well, Italian. There may well be other more local sights to visit which experienced Italian visitors would be aware of.
I enjoyed my relaxed day with no time pressures. With those timings I'm not sure that I would try to do Rome under my own steam.
I know it is very counter-intuitive not to go to Rome, but my preference was to leave Rome for a day when I would have time to give it proper attention.
You face a similar issue at Palma, with a 1pm arrival time, as the port is a couple of miles out of town- eating into your precious shore time. You won't be into central Palma until maybe 2.30pm, then have to leave again around 7pm back to the ship. Time enough for the city, centre but a bit tight to go further (say Soller as an example) under your own steam.