If you're debating where to stay and here is one of your options, just book Soula's place.
Lovely apartment, great view, very reasonably priced and in an IDEAL location. Only 20 minute walk from the acropolis, and just as close (20-30 minutes) to some of the best restaurants and bars in all of Athens, as well as most other landmarks. It is also only a couple minutes away from the metro which means you can be down to beautiful Vouliagmenis within an hour of leaving the apartment.
Soula is a great host, very quick to respond to messages, very kind, and even left some beers and deserts in the fridge for us which really warmed our hearts.