This is an excellent place, hosts Danai and Ilias are very thorough (see the directions and online guide) and were 100% responsive, on-time and courteous. All essentials were there and the place was very clean. We can support all the positive comments in the previous reviews.
We stayed 4 nights with our two kids age 10 and 12. We were able to walk everywhere (just be super careful with kids crossing the streets). We used Ilias' detailed Metro directions to get to and from the airport (although, with 2 adults 2 kids it is 23 Euro, so you might want to pay 10 more for a cab). The neighbourhood is great, right at the south slope of the Acropolis. It doesn't seem as touristy as the north side (Plaka) and we enjoyed the local cafes and shops. Pass by the touts at the restaurants right outside the Metro, there are better places closer to the apartment. Manh Manh restaurant (from Ilias' guide and also a Lonely Planet choice) as well as Strofi and the cafe right across the street from Strofi were terrific. The kids loved the renovated Olympic stadium (walking distance) and had fun running the track.
Thanks Danai and Ilias, we had a lovely (if too short) stay in Athens!