I would highly recommend Athina's place. First, staying in Koukaki rather than the more touristy Plaka was a very good decision. It's quieter, more normal, and the food is fantastic and inexpensive. Great little cafes and restaurants almost around every corner. The location allowed us to walk to virtually ever destination in the center of Athens, including The Acropolis & Museum, National Garden, Plaka area, etc. It's also very close to several bus stations and the subway, which we used extensively.
Some other very nice touches - We brought small children, so Athina had a portable crib already set up for us as well as children's plates, bowls, and silverware. In addition, she scheduled a taxi for us on a couple of special occasions, including to/from the airport. Her communication is top-notch. I don't think you will be disappointed with your stay.