May is a good month, it is warm, but not hot..
Just to give you an idea, at the moment we have a daily high of 30 C in Athens.
However the water will be cold for swimming, especially at the beginning of May. In May a bit of rain is possible, depending on which part of the Mediterranean you are.

Best time is actually in September, when the weather will be stable, and warmer as will be the water.

I agree with clausar, but prefer early June. The water is a little bit warmer (not much, though), and the weather more stable. May is actually a nice month to be in Greece, but the weather on the islands and at sea is cooler than in Athens, with the chance of an occasional rain shower. September starts out hot, getting cooler as the month progresses. After being warmed by the sun all summer, water is ideal for swimming.

When picking your cruise take a good look at how long the ship stops at each port.

Thanks for the advice! If we went with late-May/early-June, won't it be touristy? Or is it not that bad yet?

Oh and is there a rainy season in the Med?

Well to some extent, when it is nice, it will be touristy plus once the boats gear up many of the ports will have these big ships coming in with LOTS (thousands!) of passengers. That being said we have done several Med. cruises and for the most part the crowds don't spoil the experience, just realize you will have to be part of a throng and plan how best to deal with it. Unless you have the $$$$ for the super pricey small ships that go to smaller ports but fear not, you can have a wonderful time on a mainstream ship!

I really recommend the Rick Steves guide to Med. ports - excellent tips on what to see and how to deal with the logistics of the many different ports. You may want to book small group port excursions with others you "meet" on your roll call - that can minimize the crowd issue. Many of he ports are very enjoyable / doable on your own. Also as an earlier poster has said, pay attention to the time in ports - the more time, the better - it does take some time to get off the boat and make your way to the sights.

Start checking out ships and itineraries on Cruise Critic - you can be reading the reviews from this years traveler's on Med. cruises - this will give you lots of ideas on what to do and any problems that might be involved weather wise / crowd wise. Best of luck to you and your husband!

It won't be touristy.... but imagine a huge cruise ship arriving at the port of Santorini, which has a tiny main village, and some other smaller ones..... The cruise crowds are enough to fill up the narrow streets of Fira, for instance.....

In Western Greece there might be some rain, otherwise it will be warm and sunny
There isn't a rain season, like in the tropics... but it rains a lot more in the winter, while climate is dry in the summer.

No, it won't be touristy. The Greek Islands only begin to get busy when Scandinavian and German schools start their summer holidays in mid to late June & July. August is the traditional holiday period for many countries. Cruise ships have a longer season, but only stop on a few islands with deep water ports, e.g. Corfu, Rhodes, Santorini, Crete. It's busy for a few hours, but when the cruisers get back on their ships it is peaceful again, especially in Oia on Santorini.

I have visited Greece in all the months between May and September (clausar Lives there) and it rarely rains June - August. The rain in May and September is sporadic, and won't ruin your holiday. Chances are it won't rain at all while you are there. In May and late September you will need a jacket or sweater for the evenings.

We did an Eastern Med cruise plus land tour last year, end May/ early June and it was pretty hot, especially during the day, though the sea was still a little chilly to swim. But we had brilliant blue skies and the crowds were manageable, though as clausar and Heindall say, 3 cruise ships in a small port like Santorini can mean 6000+ tourists!

The Med is simply gorgeous, very port intensive, try and get together with people from your roll call for private tours, way better and cheaper than the ship's shorex.

Have a great vacation!