We loved our stay at the Theater Apartment - while it is not necessarily walking distance from the center, you have several options to get around quickly with public transport.
The apartment is amazing - very well equipped kitchen (with nice Nespresso machine and coffee provided to get you through the day), amazing huge bathroom (bathtub with whirlpool 😉) and the entire place feels well put together and homey. The hosts are also very nice and responsive.
The only downside was that we didn’t really have bath supplies (shower gel, shampoo).
Nonetheless, we warmly recommend this place for a super comfy stay in Vienna! ❤️