July and August are fine if you are prepared. This is the time most people come to Greece because this is when most people have their holidays and what could be better than to be close to the sea during the hottest months of the year? It's more crowded and rooms on the islands are harder to find, but the island nightlife is jumping and the beaches are lively.
Advance booking is the best way to get cheap flight to Athens. Book 4 to 6 week in advance to grab cheap flights. Airlines such as British Airways, Scandinavian Airlines and Swiss offers great discounts on airline tickets. From the airport you can use A direct link rail transport, Athens Airport Shuttles, Athens Taxi service transport, Athens Metro and Bus.