If you want to have great, simple and cheap place to stay in Athens go there!
The view is great and you could not be more central in the city. The apartment itself feels more like a personal cosy home with a lot of little things inside. It has everything that you need. A lot of stuff to cook and big fridge, towels, ... . You don't have to buy a travels guide before ;)
You would also have the opportunity to use two bikes. The father of Dimitris is a very kind person and getting the keys there and things done a very uncomplicated.
If you like to be over the rooftops of Athens in a simple artist kind of apartment then go there.