July and August are certainly the most popular months of the year in which to visit Athens however for some it is not possible to get away until September or later.
Depending on the industry you work in you may need to be available during the peak summer months. Many businesses rely on earning their money during the summer making the idea of getting away for a few weeks impossible.
The good news is that holidaying in September can work out a lot cheaper. There is less demand for accommodation meaning lower prices and greater choice. The same of course can be said for Athens car hire with the high demand of the summer season dying down. There are excellent September bargains available for those who care to look.