You could charter out of Athens, there are loads of companies operating there, and then explore the Saronic Gulf. Despite what others have said there is no meltemi in the Saronic Gulf, winds are usually light but enough to get you moving. There is plenty to explore - Epidavros (including the Asclepion and theatre), Angistri, Aegina, Methana, Poros, and if that's not enough you could
head out to Hydra and Spetses.
A week isn't long to explore the area and if you're looking to mile build you probably want to do a one way charter out to the Aegean islands, then you may have to deal with the meltemi and struggle to get back to Athens.
August is hot hot hot and busier than other times, but the Aegean/Saronic etc is much preferable to the
Ionian, where you will feel as if you are in a
trailer park at that time of the year!