We just came off the Jewel of the Seas Suez Canal, repositioning (11/30/19-12/16/19; Rome to Dubai) and have visited other ports on your list over the years with different ships and cruise lines.
Civitavecchia is your gateway to Rome ... but the port is at least 45-minutes bus ride into the city. If it is your first visit to Rome, your best bet would be one of the ship's excursions, likely a full day tour (7+ hours). Read the excursion menu carefully, determine which tour meets your interests best, and book early.
Kusadasi is your gateway to Biblical city of Ephesus. Again, book a ship's tour!
Piraeus is Athens. The port is very close to the big sites, museums and shopping. Take a ship's tour or make private arrangements. While there is always concern with private arrangements for getting back to the ship on time ... you'll never be terribly far from the port. We did a ship's tour last month ... but felt we could have been successful on our own.
Santorini: We booked a ship's tour for our visit last month that included walking through two old villages, a visit to a distillery, return to the main center with a one-way tram ticket back down to the old port. I'm don't drink but found the entire tour very pleasant. Loved it! Can't wait to return. One could easily visit the city center and shopping w/out a ship's tour ... but I'm glad we booked the tour.
Edited to add: One curious thing to consider, one might have difficulty guesstimating the impact of jet-lag. For me, on the recent trip, it hit hard on day 4, Piraeus/Athens. I was a woozy mess. Just as glad, I suppose that we under the shepherded care of a ship's excursion ... as I wasn't thinking clearly. It hits each of us differently ... just keep that in mind and be patient with one another.