We spent 4 days in George's apartment in Psyri and it was perfect to get to know the city. It's super central, directly situated in one of the nightlife districts, so if it's your first time in Athens this is the place because you can either walk South to the sightseeing spots or Northwest /-east to the bit more chilled neighborhoods..
The apartment is in good shape, clean and nicely furnished. The terrace is gonna be your place for the first coffee in the morning or the first drink before going out. We even enjoyed a street band from up there - looking over the old town to the Acropolis!