Psyri is still underrated as an area to stay in Athens but is easily the best part of town. Everything is close by and accessible on foot, some of the best restaurants and wine are so close that you could physically crawl home, and the Acropolis can be a quick 8am morning walk to beat the 9am crowds!
Place had a balcony which was pleasant and the apartment was extremely quiet and a pleasant stay. As for the neighborhood, it looks sketchy, but is nothing of the sort and is very safe.