We just got off the maiden voyage of the Emerald Princess. What a wonderful cruise! It did all of your ports except Sicily. Here's what we experienced at the different ports.
Mykonos - We were perfectly happy taking the free shuttle bus into town to see the sights on our own. It was very cool and windy the day we were there. The people who went to Delos got very cold.
Kusadasi - We took a great Princess tour to Ephesus and the Terrace Houses (not to be missed!). I think this might be a good place for a private tour that would allow for more time at Ephesus. Save time for the Kusadasi Bazaar. We had a very good time there bargaining with the friendly merchants. (Glad we brought an extra suitcase!) The bazaar was a 5 minute walk to our ship. Ephesus was about a half an hour drive away from the port.
Santorini - DH did the volcano walk & I went on the Oia and Fira (aka Thera or Thira) tour. We would do this port without a tour next time. It was a very beautiful place. We used tenders there. They dropped you off where the cable cars and donkeys are located.
Rhodes - We found a wonderful taxi driver in Rhodes named Themis. He took us all over Old Town and the island explaining sights and telling stories along the way. Thanks to him, we have wonderful memories of Rhodes. The email address he gave us is firstname.lastname@example.org
Interesting things are spread out around the island. You can easily walk to Old Town but itís a long ride to Lindos.
Athens - We were glad we took the Princess tour of the Acropolis and Corinth Canal. We were one of the first tour groups to reach the Acropolis so it wasnít very crowded when we arrived. Traffic was a nightmare in the city. Some on private tours had a less than perfect experience. Our lunch stop at a beach resort along the way was very nice. The trip down the canal was a relaxing break from all the walking. The ship docks about an hour drive from Athens.
Naples - We did the Sorrento, Pompeii and Capri tour last year with Princess. It was very good. We did the Hop-on Hop-off bus this year as we wanted to go to some of the museums. We needed a relaxing day after traveling from the State the day before. The people who took private tours to the Amalfi coast were thrilled. There is a castle right across the street from where our ship docked.
Rome - We had one day in the middle of the cruise for Rome last year. The Elite Princess tour that included Vatican City was very good. Iím glad you have the extra time to explore on your own. The ship docks a long way from Rome.
Many of your stops have difficult walking conditions. Even when dry the paths are slippery. Some are very steep and uneven. Bring shoes that grip walking surfaces.
Hope something here is helpful. Enjoy your cruise!