Well, generally speaking the best time to visit Greece is middle of June middle of July
The prices are still not that high, the weather is good, not a lot of tourists around.
If your prime concern is diving and not swimming, sunbathing or having a busy nightlife, late May and September is also a good choice. The prices are even lower and the weather is usually nice. Still, it can be risky, since the weather is unpredictable at these periods
August is the most popular time for holidays in Greece, which means high prices and crowded places.
Of course, as far as weather is concerned, it very much depends on where you want to go. For instance, Crete has a higher temperature, summer begins in early May and ends in late September, and has a lot of diving sites. Cyclades islands (Santorini, Myconos, Amorgos etc) have also a long summer, but in June or September can be very windy, which means poor visibility. Chalkidiki, on the other hand, is at the north, so I would not recommend it for May or late September
Still, I have to warn you that, like at the rest of the world, the weather this year was peculiar. Taking Chalkidiki for instance, - this is where I usually dive - May was hot and shiny, but June was like autumn. I had hardly any dives in June since it had a lot of windy and rainy days, and the visibility was not good at all.
I would love to give you moire information for diving sites and holidays in Greece in general, but it would help if you told me what place or type of holidays you have in mind.
In nay case, I hope you will come and I am sure you will have the best of times and dives!