I highly recommend staying at Christos's place. He really cares about his guests. There was a refrigerator in the room and he made sure we had everything we needed for a nice breakfast in the room before exploring the city. Everything was clean and nice, and Christos is a very warm and friendly person. Only thing was, that the room was very hot because of the heat – but he made sure we had a fan to use at night.
It's a bit away from the city center, but we just took the metro. By metro and walking it took around half an hour to get to Stephansplatz.