I can only recommend this apartment. I think this has been one of our best AirBnB experiences so far. The location of the apartment is excellent, it's a one-minute walk from the the Stephansdom away, yet it's still quiet - especially at night. The apartment is both charming and practical at the same time. Kitchen and bathroom are modern and very convenient, while the rest of the apartment has still maintained it's old Viennoise atmosphere. Andreas, the host, was very friendly and welcoming and throughout the apartment, there were little thoughtful tokens (e.g. a welcome message, coffee capsules for the Nespresso machine, travel books about Vienna, DVDs and so on). In general, the apartment had pretty much all the amenities we could think of. E.g. there is a large TV in the living room as well as a smaller (but still rather large) TV in the bedroom, which was very nice. We had asked for a baby bed and Andreas had not only provided that, but also made sure that there was a pillow and blanket as well as a baby chair ready for us; something that is often forgotten. Last but not least, the apartment was really very clean, which we appreciated a lot.
Long story short: We 100% recommend Andreas' flat.