A good accommodation near Metaxourgio metro station. The first day we had a nice lunch at Seychelles, which I recommend. Then we walked down to Psyrri and ended up at Hadrian's Library in Monastiraki, from which we enjoyed the impressive sight of the Acropoli. From that very moment, we really enjoyed the position of the apartment. The quality of the apartment is also good.
Unfortunately, in Athens, it is not rare to find abandoned buildings and some narrow streets can look scary, especially if some gentleman walking down the street is enough sloppy to trigger all possible prejudices. However, all in all, I felt very safe, despite many comments online describe several neighborhoods as dangerous (while not reporting any crime). Maybe, it is better not to visit the city alone. But, Athens is enchanting and it must be visited at least once in a lifetime.