We were in the eastern Med last November. Most days were in the 75F range and very pleasant. There were storm systems over the western areas, but they missed us until the very last afternoon. It was perfect weather for the many shore days.
We were on the Noordam, and were very pleased with the ship, despite reading many criticisms of it beforehand. It's an older ship, so if you prefer the more contemporary facilities, try one of the newer ones; we were very happy with it. We were very pleased by the service, the crew were great and the food was uniformly excellent. [Our habit is to book the lowest cost outside cabin, and happily accept whatever upgrades are offered.]
We booked two back-to-back cruises, for a total of 20 days. The itinerary on the return section was to include 2 days in Israel, canceled because of the violence there. It was Rome - Naples [Pompeii] - Heraklion [Knossos] - Santorini - Athens - Mykonos - Kusadasi [Ephesus]- Istanbul [2 nights] - Alexandria [Cairo/pyramids] - Limassol, Cyprus - Rhodes - Kusadasi - Malta - Messina [Taormina] - Rome. As it was our first foray into the Med, we planned ahead on an "ancient ruins" theme and did not regret that at all. We also found that given the incredible number and diversity of ports, one-day shore excursions were sufficient for a decent taste of many places we know we will return to someday for extended stays. The fact that I can still recite the itinerary and shore trips from memory - and the fact that we have 4 bulging photo albums to inflict on our friends - says that it was one incredible experience. I'd be happy to comment on any of the ports and shore trips that you might have an interest in.
If you are thinking about a Mediterranean trip, think carefully about what you most want from it, then take the time to check out itineraries, length of port stays, shore excursion options [we have learned to trust HAL's descriptions, for example], and ships. Don't try to do it all - there's just too much, and you'll want more anyway! There are plenty of choices, so you can find a good fit. We also found that doing a lot of reading and planning was fun, and paid off in not wasting time with things that would have disappointed us. Finally, it ended up costing us somewhat more than originally planned - but we have regretted not a penny.