Well, you need to consider that you can easily do some of these places on your own (and save lots of money). In the case of Ephesus, we strongly recommend booking a private excursion with a reputable local tour company such as EKOL (we love this company). Even if you have a very small group (such as a couple) the cost of private excursions in Kusadasi is usually cheaper and much better then what you get through the cruise line. All the local tour companies will meet you right at the port terminal building (they will have a sign with your name). You definitely want to go to Ephesus + include the Terrace Houses (not included in many cruise line tours). Going to Ephesus and not going in the Terrace House exhibit is like going to the Statute of Liberty and not going inside!
In Sicily we assume you are going to Messina and you should go to Taormina. If your cruise line has an option for transportation only (no guided tour) this is a good option since Taormina is a place to walk (only has 2 major streets), browse, visit the Amphitheater (anyone can pay to go inside this ancient place), etc.
On Rhodes you will dock in Rhodes Town and you can easily explore the old town on your own (all within walking distance of the pier). Many like to take an excursion to the ruins at Lindos and this is a personal thing. When we are on Rhodes we do what most of the vacationers on this island do which is to go to the beach (they have many very nice sandy beaches).
Santorini - Much depends on how long you are on the island. If you go on your own you will be tendered into a a tiny place below the cliff-top city of Fira from where you can take the cable car up..or if you are a bit crazy you could opt to ride up on donkeys. Fira is fun for just walking, admiring the views, eating and shopping. Many visitors like to go to Oia (another cliff-top town) which can be done on your own by taking the local bus or a taxi. When we have a long port day here we will often rent a car and drive all over the island enjoying some beaches, going to a winery, etc. A rental car will usually cost about $70 for the day and if you have 4 in the car (or even 2) its a pretty cheap way to enjoy the entire island.
Mykonos - If you are interested in ruins you can take an excursion to nearby Delos. Otherwise, Mykonos Town is good for shopping/browsing and a drink/snack at one of the nice cafes. The island is famous (in daytime) for its sandy beaches and we usually take a local bus (costs less then 2 Euros) to Paradise Beach where there are plenty of facilities and chair rentals.
Athens - This city speaks for itself and can be done with an excursion or by simply taking the train/subway from Pireaus into Athens and doing the same stuff on your own (at considerable cost savings). A good guide book such as Rick Steves is a must for the do it yourselfer. Of course everyone wants to go to the Acropolis and walk around the tacky Plaka district (both included in most tours).
Naples - Too many choices to deal with here. You need to make choices. Every option can be done on your own with the exception of the Amalfi Coast. For a first time visitor the best way to see the Amalfi Coast is to arrange for a private tour since most of the cruise line tours use large buses which are not permitted to enter Positano (you just get to see the town from the road above).
P.S. If you think you are overwhelmed imagine how we feel...soon to leave on a cruise that has 31 ports. :)