I've always found these guys excellent: https://yacht4less.com/
I can recommend the Argolic Gulf area – Aegina (easily accessed from Athens) to Poros and down the eastern side of the Peloppenese. Hydra tends to get very crowded in summer (you need to be in by early afternoon to get a spot) but there are plenty of quieter spots to be found. Nafplion is quite a busy city but worth a visit and there are a number of places on the coast between there and Monemvasia at the southern tip. Astros, Plaka, Ierakas, Kiparissi, Ermione spring to mind.
Aegean Sailing School also do charters but I find their prices a bit on the high side. They do tend to have newish boats though and they look after them well – they're not a huge outfit.
I'm sure you'll get plenty of other recommendations too. I'm especially looking forward to exploring the Ionian.