FROM AIRPORT

By TAXI (approx. 20 minutes):
If you order a taxi in advance (few days before arrival), it will wait you in the arrivals. Few companies do it at different cost:
taxi http://fixtaxi.com/ (25 euro) +4316021240 (online reservation available)
taxi Rosenov (29 euro) +4314857777
taxi C&K (29 euro) +43144444, they also have those office at the airport
regular airport taxi will cost you about 32-36 Euro.

By TRAIN (approx. 30 minutes, 1 change):
There is a local train S7 and S8 (S-Bahn) 25-30 minutes (cost 3.40 Euro). Make sure when train leave it shows "Wien Mitte," "Wien Nord" or "Floridsdorf". You have to exit the train at station “Rennweg”. From there you walk (5 minutes) or you can take tram O (only 1 stop), in direction Sudbahnhof (2 minutes), exit at stop "Kolblgasse".
Take a walk up along the Kolblgasse for approx. 2 minutes till you reach the Apartment.
NOTES: be carefull at the airport, and DO NOT take CAT-train (CAT-train is not stopping at the intermediate station Rennweg), CAT train leaves from another platform than the local train.

Alternative (approx. 20 minutes):
Reserve a CAT-CAB service that combines a package of express City Airport Train (CAT train) and a taxi ride till the house door (or pick up when you leave), total cost 24 Euro for up to 4 people: http://www.cityairporttrain.com