I have had the pleasure of cruising many times in the Caribbean, and once before on the Eastern Med. My FAVOURITE cruise hands down was on the Odyssey of the Seas from Rome, 8 nights visiting Santorini, Kusadasi (Ephesus), Mykonos, Messina (Sicily), Naples and then back to Rome.
Arrive a day or two early into Rome and make sure you see all of the sites. Stay "inside the wall" (I agree that BNBs or AirBNBs are a good option, but be careful of the stairs that you may have to take especially with large bags!) and make sure you book tickets to the Pantheon (museiitaliani.it) in advance, as well as the Vatican Museums. I recommend a tour guide for the Vatican Museums, but book it directly from them and not a third party reseller. If you can get reservations before hand, try out Sora Lella and La Gattabuia for authentic local cuisine!
We used a private van service (rometransferservices.com) as we had a lot of baggage. They were excellent drivers and very friendly, and always punctual!!
If you are going to Naples, and want to see the Veiled Christ, book online at museosansevero.it beforehand. Tickets sell out!! And try out 50 Kali for authentic pizza.
Mykonos, we went to a quiet beach called Agrari. It is a bit more secluded, and quiet. But excellent services. There is a hotel there with a beach club that sells 2 chairs and an umbrella. Well worth it! Use the local app called iMove Taxi app...download it on your phone and use it like Uber. Uber doesnt really work on Mykonos.
Santorini, I recommend that when you tender, dont wait in line for the cable car. Instead take a water taxi to Oia, and spend the day there. At night, book the restaurant Oia Gefsis for sunset (google the time for your date of arrival and make sure that you book online to catch wonderful views of the famous sunset).
Ephesus - I recommend that you take a tour organized by Royal Caribbean.
Sicily (Messina) - I recommend a day at the beach at a place called Giardini Naxos. You can grab a private car on the street outside of the cruise terminal, and negotiate a 4-5 hour transfer. They will drive you there, stay with you and bring you back. It's a lovely town where the locals relax. The beach club we visited had a restaurant and nice chairs.
Make sure you taste the Gelato and Turkish Ice Cream at each step of the way!
Enjoy!
