About the Greek Islands
There are 227 inhabited islands in the Aegean and Ionian Seas (Greek Tourism Organisation), gathered in six island groups. Each of these islands have their own culture, atmosphere and local specialities, providing us with a very rich tapestry to sample from on our journeys. Their unique cultural histories are also visible in the numerous archeological sites and musea. Other islands have a spectacular geological history, for instance Santorini
What are the best times to visit?
It is hard to answer that question as it depends where you want to be and what you want to do. Some indication for the climate of the Cyclades region: max. day temperature over 20°C between mid-April and mid-October. Water temperature over 20°C between mid-May and end of October, peaking at 26°C around August. Between mid-July and early September most of the regions are very busy making money in mass-tourism and day temperatures can hit the lower-thirties. It just takes a bit more effort to find the quiet out-of-the-way bays. The below graph from climatemps.com gives a good overview of what can be expected. More weather info can be found here.
Apart from climate, the various festivities are another factor in choosing your time to visit. For instance, the Easter weekend is celebrated with spectacular festivities in Greece. In 2017 it falls on April 16 and on April 8 in 2018.
"Let Easter be the release of the soul out of its tomb of ignorance, worry, fear, anger, hopelessness"
You can find more on Greek festivals on the web, for instance here. Please note that some festivals (e.g. Easter) fall on different dates each year. Unless the year is mentioned, be careful when relying on web site dates.