Koukaki, just south of the Acropolis, has emerged in the last decade as the best place to stay in Athens for travellers who want easy access to the major sites without the constant tourist crowd of the Plaka. The neighbourhood is genuinely residential — Athenian families live here in solid 1930s apartment blocks — and the pedestrianised Drakou Street off Syngrou is the social spine, with cafés and small restaurants spilling onto the pavement.
The Acropolis Museum and the south-slope entrance to the Acropolis are five minutes' walk away. The Syngrou-Fix metro station puts you anywhere in the city quickly. Walk up to Filopappou Hill at sunset and you have everything you need.