I rented an apartment in Pangrati neighbourhood, which was really safe and the rent was not too expensive. Airbnb works well for short rents in islands, or in the mainland. I really loved my neighborhood, because it was close to the historic centre (25 min by foot to the acropole) but still quiet, without being inundated with tourists.
For accommodation, we went through an agency that is well known by students. For research we spoke to Marina, who speaks very good French. (Agency name : Unlock Athens-www.unlockath.com)
We rented a flat (40m²) for two with two big bedrooms in the neighborhood of Pagrati.
I was staying next to the university, 25 minutes walk (easy to access, no problem with bus/metro transport). The airbnb was really very very nice (Chanion 8, Ag. Varvara 123 51, Greece).
In addition, I was close to the Ag. Varvara metro stop.
I stayed near the Kerameikos metro station, and the area was calm and safe. It only took me 10 minutes on the metro to reach the city center at Monastiraki. Near my apartment, there was a lively street filled with bars and nightclubs.
