My wife and I stayed at Akis and Marietta's place. It is located in a great area that is safe and walkable-- it was very convenient to get to areas such as Mount Lycabettus, Syntagma Square, and Monastiraki. We felt comfortable in the apartment as there was everything we needed.
Akis and Marietta went out of their ways to make us feel comfortable and welcomed and we would totally recommend their place for a short or extended stay in Athens.