We have stayed for four nights in the flat of Josef and Celine and we have enjoyed it. The flat is as shown on the images. It is small but because of efficient use of space it didn't really bother us. It made the flat itself a worthy experience. Celine did both check in & out it and that went very smoothly. The fact that there was no wifi available was not much of an issue (except to check the availabilty of Citybikes!), because Vienna has numerous places with free wifi.
The flat is located close to the Thaliastrasse and Burggasse metro stations. At both stations you also have a Citybike station. A few minutes walking on Neustiftgasse towards the centre, there is Marks - a restaurant which also serves breakfast (worth a try).