From the moment my girlfriend and I arrived we were in love with Nancy & Nasir's place.
The perfect balance of rustic looks and comfortable amenities. It was our first night in Athens, so it was important for us to be in a place that felt safe, had reliable wifi and was accessible to the city (the subway ride is only 10 mins to most tourist attractions in Athens).
Nasir checked in via email each day, and had advice on where we could eat in the neighborhood (For american food try XOM, there are also a few small authentic greek spots to enjoy)
You save some money by keeping out of the downtown core and hotels, if you don't mind a little walking and want to have a more local experience this is a great option for you. After one day you will be comfortable and familiar with the neighborhood.
We hope to return again one day!