Personally my favourite time to visit Greece is in mid to late September. The weather is not as hot as in the peak travel months of July and August, airfares and hotel rates are slightly cheaper and the crowds have thinned out somewhat by that time. Clearly the best time to travel to the islands would be in the peak months of June to September specifically because of the weather. Most of the islands are fairly quiet in the off- season except for local residents. It is true that you could save considerably on airfare and especially your accommodations in the off -season but, the islands are not the place to be when it's cold and rainy.
Please keep in mind that Greece is now part of the European Union and therefore uses the Euro for its currency. As you know the US Dollar is very week versus the Euro, which means that Greece is no longer considered an inexpensive travel destination. This in turn has had an adverse effect on tourism to Greece the past few years. It does not mean you won't get your money's worth only that the prices are more on par with those in Italy and Spain which were typically more expensive destinations than Greece.
