We've been to Sorrento before and this is a very walkable town and also the starting point to see Pompeii and the Amalfi Coast. You need to tender in and negotiate the uphill climb to town. Prices are high but not as high as other Italian cities. Beware of the dishonest bus drivers that take you up the hill!!!
Great port and everything can be done on your own. You need to catch the tram outside of the Port Area and from there you can access all of the city. I would suggest that you get on a bus and get hopelessly lost and experience the wonderful Turkish Culture.
I would suggest that Azamara spent less time in Chios and have have two full days in Istanbul.
We booked with others from Cruise Critic and saw the fabulous museum, St. Paul's, Church, the house of Virgin Mary, Ephesus and the Terrace Houses and brunch. Our guide was highly recommended on Cruise Critic and the cost of this eight hour plus tour was $55/person. If interested contact firstname.lastname@example.org and request Bulent Orkus as your tour guide.
Cyprus is divided into two parts. One part is Greece and one part is Turkey. We saw Limassol (Greek Part) and this is a very pleasant port with not much to see in town. If you have more time you can go to the divided capital of Nicosia and some of the other historical sites. We had to leave at 1:00 PM and could not explore this divided country.
Egypt is an assault on all your senses. This is a wonderful third world country where 65% of the people are unemployed. We took a very long day trip to Cairo to see see the Pyramids, Sphinx, the Egyptian Museum, and the Grand Bazaar. We started out at 7:00 AM and return at 8:45 PM. We were nearly the last to board the ship but it was a wonderful day. We booked with Ramses Tour out of Alexandria and the cost was less than half of what the ship was charging. I would strongly recommend Ramses Tour!!!! And we didn't have any carpet or papyrus hard sells like the tours from the ship.