June through September is considered the high season, however May and October are ideal months to travel to the Greek isles offering both ideal climate and limited crowds.
It’s recommended that you limit your Greek Island choices so that you can truly enjoy your trip instead of trying to see too many making you feel like you are on the run through out your stay. The rule of thumb is more days, more islands so that it flows nice and smooth, but generally speaking 2 to 3 maximum plus a night or two in Athens works out perfectly.
Pictures are worth a thousand words as the old saying goes. Here are some Great links to immerse yourself in the Greek Islands.