We (family of 2 adults and 2 children (6 and 11 years old)) had a great time in Athens at Alexandra's place. The apartment is cozy, has everything you need and it is situated close to the main attractions (as Acropolis, Plaka, Monastiraki, National Gardens, Syntagma Square etc.) where we walked to. It is also close to bus/subway stations, if you need.
I surely recommend Alexandra's place.