I was in your shoes last year; I planned our family cruise this past May. We actually booked the Princess first but cancelled and switched to Celebrity because of the Itinerary and how long we would be in port. From what I remember, Princess had Mykonos, Istanbul, and Kusadasi. But Celebrity had Santorini and Dubrovnik which the majority of my group opted. I think either of the ships are fine, but you need to decide what’s more important, the ship or the itinerary. And if you can’t decide, think of the cost.
There’s a lot of places to stay in Rome, I guess it depends what you’re looking for. Here are some that I know are recommended. Hotel Mozart (near the Spanish Steps), and Hotel Alimandi (near the Vatican). But check out www.Venere.com
for hotels and then read the reviews on tripadvisor.
Here’s my experience with the ports you mentioned:
Mykonos – DIY by bus or rent a car. This can be a beach day if you want. But if you want to see more archeological sights, take a boat ride to Delos Island. It’s about a ½ hr ride from Mykonos. Or just explore the town of Hora which is Mykonos’ capital.
Istanbul- I would do a private tour here, there are so many things to see and do. The Grand Bazaar was amazing, and if you or anyone in your family loves to cook, definitely visit the Spice Market. Have lunch/drink at Beyoglu which is an area that has a lot of restaurants and shops. An interesting tour would be the Harem & Treasury in Topkapi Palace.
Kusadasi – I would suggest taking a private tour here too. A cool pix to take is at the Latrina which is the oldest toilet in the world w/your kids doing a sitting pose on it.
. Sorry, we did and it was funny.
Rhodes- Have a pix taken at the Colossus of Rhodes which is one of the Seven Wonders of the World, definitely visit Old Town which is a UNESCO site. And there’s some really nice beaches along the coast to Faliraki and Lindos. There’s a lot of roof top restaurants in Lindos as well as the archeological sites.
Athens – we opted not to do this port DIY, because my group didn’t want to walk 25 min to the metro, I would have loved to since the metro has some amazing archeological pieces on display. A mini museum in the metro. As you move further east, the temp gets warmer/hotter. The Acropolis is an amazing site to visit; we had fun walking around the Plaka and having lunch. We even stopped at a beach for a bit.
Naples – Traffic is terrible here so we did a private driver in this port. We drove along the Amalfi Coast (stopped at Sorrento, Positano, Revello), and spent 2 hours in Pompeii. This was a pretty relaxing day; we saw and did what we wanted to do.