Veselinka's place is cozy, clean and perfectly equipped for a shorter stay for either a couple or two people who need separate rooms (though getting along well is probably a requisite, as the common areas are smallish :)). It is located within a walking distance (under 10 min) from a big train station, Rennweg (from which the S-bahn drives direct to the airport in 20 minutes--so that's perfect), and perhaps 30 minutes strolling walk to the downtown. There is a park nearby that's quite nice for a walk and has a very decent Austrian-cuisine restaurant, as well as a few supermarkets, stores, a pharmacy-- so basically all you need.
Veselinka was very helpful, answered promptly to every inquiry and accommodated us quickly.
The only thing to keep in mind is that the apartment does not get much direct sun, so in spring (when we went), with the heating off, it can get a bit chilly, so bring cozy warm slippers! Otherwise, a good choice!