We took the ship's "Walk the Line" tour into northern Cyprus, which we enjoyed. Crossing the "Green Line" into the north was quite an experience. This is a port where it pays to take an organized tour.
We booked our own private driver with two couples we met on Cruise Critic. This ended up being cheaper than the ship's tours and a much better experience. This was our first trip so we hit the highlights on a similar itinerary to what the ship's tours did. Sites in Israel tend to be fairly crowded as it is and it is easier to go with a smaller group. We felt quite safe throughout, even on the West Bank in Bethlehem. We used Alon Israel tours and were very satisfied with our guide. We did two one-day tours rather than stay overnight in Jerusalem; one could probably see more with the overnight but it does add to the expense.
We found Egypt fascinating, but a guide is a must. We used DeCastro Tours and had our own driver and guide. Would highly recommend. We went from Port Said to Cairo, overnight in Cairo (this is a must, it is a long drive) and then back to Alexandria. We skipped the Nile cruise, but did take the Cairo subway (surprisingly clean and orderly compared to the rest of the city). Don't stint on Alexandria; it is quite different from Cairo and worth seeing in its own right, particularly the catacombs which were one of the more interesting things we saw on the trip.
We took Ekol Tours to Ephesus. Not really any cheaper than the ship's tour, but we had our own guide and driver and got to see what we wanted. They took us to the ceramics and carpet demonstrations, which were (relatively speaking) more laid back than the bazaar atmosphere; if we were going to get a carpet we probably would have gotten one there.
Istanbul is quite interesting. Unfortunately we hit some terribly cold and rainy weather. It is fairly easy to get around on the tram, but once off the main streets there is insufficient signage and what there is is hard to read. We had better luck walking around in Cairo! The Grand Bazaar is not as intimidating as you might think. This is a port you can do on your own, although with luggage you will want a taxi.