On our 11 nt Eastern Med Celebrity cruise we visited each port and did most of the listed excursions basically on our own. The fees they charge are exorbitant and unnecessary (all but one).
The exception was Ephasus from Kusadasi. The excursion included transportation, the Virgin Mary house, a guided tour of Ephasus, and lunch. There was really no way to do that logistically on your own.
Istanbul was a joke. The excursion gave you a ride into town and showed some of the sites. We opted to do that on our own but took the 10E bus ride offered by the ship because they said it was too far to walk. It seemed worthwhile because it took so long to get there. Once in the city it was easy. A local (carpet salesman) saw us taking pictures and started talking. He showed us the way around, got us into the Blue Mosque (no line), and gave a running history account. Then afterwards he asked us to see his wares. We gave the shop a curtious 2 minute look. Said we were not interested and left. No hassle. The problems began with the return trip. City traffic is unbelieveable. We got there 30 min early as instructed. Then the bus was over 1 hr late arriving. Then it took over 1 hour for the ride back to the ship. There is a train you could take for a couple of lira that stops in front of the port and in the middle of the city. Very fast. Or, as we did on the second day, you could walk. It only took us 20 minutes from the dock to the Grand Bazaar. We would have still been waiting to board the shuttle bus.
In Athens we took the train from Piraeus to the City for about 2E. Because of where the ship docked, it turned out to be a long walk to the station. It is very easy to find, just keep the water on your left and go all the way around the harbor. Once there, we walked up to the Acropolis, obviously, wandered through the city, and saw a few other sites. Very easy on your own and a nice train ride.
In Mykonos they recommended a bus ride (again at a cost) to town because the curvy and narrow road was not safe to walk. It is not far. But I would recommend the ride. We wandered the city and found the windmills on our own. We also hoped a ferry for a few euros for a tour of Delos. A highly recommended trip, but not at their prices. That is unless you want to pay 10X the cost for the same ferry ride and views just with a tour guide. We just listened to other tour guides when we wanted and proceeded at our own pace.
The best thing in Santorini was the mule ride up the hill. There are some things to see. But we just wandered through town and had a drink at a hillside (they all are) restaurant with a fantastic view.
Naples doesn't offer much in its own right. We took a shuttle to Capri and a boat tour around the island. The Blue grotto is the big thing. Watch out for prices. You can get a speedboat ride to the island for a couple hundred euro and an island boat tour for about 300e. Or just walk from your ship to the high speed ferry and then buy an island boat tour when you get to Capri. Again, this will cost you less than 10% of the personal tours for the same trip. On return to Naples we walked to the National Museum. We wanted to see some of the artifacts that had been removed from Pompeii. There are some fabulous statuary and artifacts in the Museum. But it is a long and dirty walk through the city. If you want to see Pompeii, again think on your own. On a previous trip we took a bus tour for over 100e each. We were very disappointed. The tour apparently only showed a small part of the city, in and out. You can hop on the trin for about 1e each. It takes you right to the city entrance and get the full tour on your own.
Lastly, there is Civitivichia. We took the train from the airport to Civitivichia. Then from there to Rome for a few days. Then again from Rome back to the airport. This route depends on how you are with luggage. A shuttle from the airport to the ship was about 125e. It cost us 14e each for the trains. The only problem was changing trains in the middle required going down a flight of steps and up another to get to the other track. It's about 2 blocks from the train station to the dock. You can see it on your right as you exit the train station. You could take a taxi, walk it as we did (all bags have wheels now), or there were men there offering to take the bags for us. Simple and easy. In Rome it all depends on your hotel choice. I purposely selected a hotel within walking distance of the Termini. Just be careful to select the right side of the tracks. It's kind of dirty on the back end. Or simply take a taxi. When returning to the airport, if you are far enough from the Termini to require a taxi, you might as well take it directly to the airport. It will probably cost you another 25e or 30e. But at least it is easy, fast, and not exorbitant. That is about the only time I can make that claim.
My basic philosophy is to enjoy the sites but do it wisely and save a few bucks so you can do it again or at least longer. Of course that assumes you are not working with unlimited funds. If you are, go for it all.
3X cruiser and woldwide vacationer