If touring the Eastern Mediterranean is on your bucket list I highly recommend that you do it with Royal Caribbean on the Navigator of the Seas.
My wife and I (no kids) recently returned from an 8 day 7 night cruise in October, 2011. We boarded the ship in Civitavecchia (often referred to as Rome but it is 60-90 minutes from Rome's Leonardo Da Vinci Airport depending on which method of transportation you take) for a round-trip cruise that took us first to Messina, Italy, then Valetta, Malta, Kusadasi, Turkey and Chania, Greece. The stop in Valetta, Malta was not planned. Originally the itinerary called for Athens, Greece, but due to a series a series of protests and strikes by members of their public transportation agencies Royal Caribbean (RC) made the difficult to decision to change the ports so the cruise could continue on-schedule. I commend them on their rationale and ability to pull of the change on such short notice with absolutely no impact on the guests. Many were disappointed including my wife and I as Athens was a big reason we wanted to take the cruise but RC made lemonade out of lemons.
From the moment you arrive at the port of embarkation in Civitavecchia RC has the check-in process down to a science. After the usual passport checks and x-ray scanners you're boarding the boat. Shortly after boarding you'll go through the paces of a safety drill so you know what to do in the event of an emergency. It is no fun being shoulder to shoulder with 100+ other people but at least you'll know what to do if the unthinkable should happen. Yes, ships still sink so I applaud RC on making sure that everyone onboard fully understands how to get off safely.