We had a great time at Michael's. Although we were about one hour late for check-in, he was there to welcome us with extreme kindness, introduce us to the apartment and answer any residual question. The apartment was large enough to host the four of us (2 adults and 2 children), quiet, clean, well-equipped, provided with more than enough cooking ingredients and with the added bonus of Netflix to keep the children busy at night. The area is residential and a bit off the beaten tracks (i.e. no tourists around, only locals) which is actually how we like it. Two supermarkets are within walking distance, and the centre is easily and quickly accessible through public transport.
This would already suffice to recommend Michael as a host, but then he really went the extra mile by proposing us to stay one more night for free, as our plane was leaving at dawn the next day, which would have forced us to book a hotel room at the airport. So thanks to Michael we both saved money AND got to enjoy a full last day in Vienna!