Exarchia is quite a particular neighborhood, comparable to hardcore parts of Kreuzberg, but if you are ok with it (in any case it's not unsafe) there are many nice places, Greek and world cuisine restaurants, bakeries, ice cream places, bars.
The apartment is marvelous, probably never seen so greatly renovated old apartment. Easy access with a code, without time limitations
Count on taxis if you have heavy luggage: even bus stops are far away. Without luggage a walk to Omonia or even Syntagma is easy.