Getting to the Port
First question, is Princess arranging your hotel and transfer to the port of Civitavecchia? Civitavecchia is an hour train ride from downtown Rome. Probably same by car. Might be more stress-free to bite the bullet and buy that hotel/transfer from Princess. That way you know you arent sitting at the gate to the port wondering how to hoof bags to the pier.
Around Rome
I remember you mentioning some difficulty getting down plane stairs at SXM. If you have difficulty walking, I’d suggest tours and cabs.
They have unlimited subway/bus passes, but it’s a fair amount of walking to most things. If you do want that, I would get a hotel near Rome’s main train station Termini which has subway, buses and trains to Termini and FCO airport.
There is an express train from FCO airport to Termini called the “Leonardo Express”. I found it easy to find in 2018.
Nothing fancy, but I have stayed at “Best Western Art Deco” twice. Clean, Serviceable and near the station but last time was 2018. The hotel recommended above is probably a lot nicer.
You already know the usual sights Vatican, Colisseum. I would ensure you see Pantheon. Beautiful building.
Lesser known, Capuchin Friar Crypts near Barberini Subway stop.
https://www.ricksteves.com/watch-read-listen/read/tms/boning-up-on-europeThe catacombs I saw were way out in the burbs. They conduct a few tours each day. You can ride a city bus, I dont remeber a bad walk. There are steps in the catacombs but not like subway or jet stairs that I recall. They would be last on my list of things to do in Rome if I return.
Pompeii. That port is Naples. Either a bus or hour train down to the site. Get a tour guide. You can walk all the cobble stone but its is impossible to look at a piece of paper and no is that the brothel or the bakery. Sorrento is nearby. I would do a ship tour to Pompeii with lunch in Sorrento. Capri hard to squeeze into one day but an alternative to Pompeii. If they have a ship tour that does all three, then doable.
Turkey. Probably Kusadasi. This is the port to visit Ephesus which used to be a seaport but was silted over and is now inland. Out of all the rocks/rubble of the Mediterranean, Ephesus is the most impressive IMO. A tour will drop you off to the UNESCO archeological sight and pick you up at the end where you can buy a genuine fake Rolex or Turkish rug.
St John lived near Ephesus and the right tour can show you the Church and can take you to the site of where Mary is believed to live out her days away from the town crowds of 250,000 back then. Ephesus was both Greek and Roman at some point.
Lot of shops in Kusadasi and places to get another fake breitling watch, carpet or local fare. would get a Doner Kabob before getting on the ship.