Yes! stay here! :) I highly recommend this airbnb. Alexandra is a lovely host and made me feel like I was at home. As a solo female traveler, I loved this place. The area is safe (don't get put off because of the old buildings,all Athens is like this). All the coffees shops and restaurants around are for locals, so you can have the real Athens experience. The airbnb is super clean, nicely decorated with all the amenities you need, big (I had even my own seating area), comfy bed, and awesome views from the balconies. Mount Lycabettus is very close, go up there to see the sun set or just up to the roof. I had to work and the internet was really fast and good. There are plenty of busses going to the center but I walked all the time.
Alexandra made my day, when coming back from a very very cold day trip, I found the fire place on and hot soup waiting for me. I recommend this airbnb.