This is a great apartment. Athina (Eleni’s niece) met us and spent time to show us the apartment and how to find our way into Athens and to the local restaurants and shops.
It's a 15 minute walk to the Acropolis and museum, a bit longer into the centre, but you can get local buses from either end of the road into many parts of Athens easily. We found these to be by far the quickest way to get around, though you will need Google maps to help figure out the routes. The bus stops tell you when the next buses are coming, but you will need to buy tickets or travel cards (valid for all the buses, trams and metro) in advance from stations or street kiosks. Single journey tickets need to be validated by the machine on the bus or metro entrance when you start a journey, and are then valid for 90 minutes on any public transport. 24 hour tickets are valid from the time you buy them until the same time the next day.
The next street is a pedestrian area full of bars, restaurants and a couple of bakeries that sell great pastries for breakfast, and the whole area is open late into the evening (but isn't so close to the apartment to be a bother). Athina gave us some great pointers for these too.
We would certainly stay here again if we come back to Athens.