From the airport
City Airport Train (CAT): Take the CAT until you reach Landstrasse/Wien Mitte, then transfer to the U3 undergound (orange line) in the direction of Ottakring. Get off at Neubaugasse and go out the Stiftgasse exit.
S-Bahn: Take the S-Bahn (S7) until you reach Landstrasse/Wien Mitte, transfer to U3 (orange line) in the direction of Ottakring. Get off at Neubaugasse and go out the Stiftgasse exit. Since the airport is located outside the city of Vienna, you'll need a separate single ticket.
Taxi: It's a 30-40 minute trip and is around €45. Request to be taken to Lindengasse 9.
Bus: Take the Vienna Airport line bus to Westbahnhof, transfer to U3 (orange line) in the direction of Simmering. Get off at Neubaugasse and go out the Stiftgasse exit.
You'll need a CAT ticket. Within the ticket price, you can take the train and the bus in the inner circle of Vienna.