Doris's place is perhaps a little out of the way if your destinations are the main tourist spots, but there are plenty of public transportation options available nearby if the walk to the center is a little long for you.
You do have to climb 4 flights of stairs--if that is an issue--but once you are at the top, outside the apartment you are greeted by a small indoor garden of potted plants that all together create a wonderful fresh scent.
Inside, the apartment is spacious with many windows, and you can look out onto the courtyard and street below--I was there during a cold spell so didn't use the balcony. Kitchen counter space and equipment are sufficient if you are cooking.
Doris is a quite an interesting person and has an incredible depth of knowledge about Vienna. She is very happy to provide tips and answer questions. Communication with her was generally rapid and straightforward.
In short, I recommend Doris's place.