We did a Disney Mediterranean cruise when my son was 14 and my daughter was 10.
In Villefranche, we took a train to the Marc Chagall museum in Nice. My son enjoyed it, but my daughter was a bit bored.
In Florence, we did the Florence on your Own excursion (as a precaution against arriving back late to the ship). We went to the Galileo museum, which we all enjoyed, and the Uffizi, which was underehelming. The Uffizi was under renovation, so we might enjoy it more now. The drive from the port was long, but I really wanted to see Florence. Pisa would be closer.
In Civitavecchia we did a private tour with Rome in Limo. That was definitely the right choice, since we were able to hit many highlights of the city, including the Colisium, Pantheon, Trevi Fountain, Sistine Chapel, St. Peter’s, and a spot with a clear view of 3 countries. Our guide was able to keep the kids interested even on the drive into Rome. (They fell asleep on the way back.)
In Naples, we did a Disney excursion to Herculaneum that included a scavenger hunt for kids. Unfortunately, our guide wasn’t as good as the other guides we heard talking, so my daughter didn’t feel engaged. The site itself was very interesting.
As others have said, a Baltic Cruise (which we did 2 years later) typically requires less time to get to excursions or interesting places, so it might be a better choice for younger kids. We don’t regret doing the Med, though.