There is an express train station at the airport: the S7 line takes you to Wien Mitte station in 25 minutes. (costs € 4.40).
A faster option is the CAT (City Airport Train), which takes 16 minutes to the City Air Terminal Wien Mitte station. This costs between € 10 and € 14 per person.
From Wien Mitte station, you have a direct underground connection (line U3 in the direction of Ottakring) to Stephansplatz station (2 stops). Once here, follow the signs to "Ausgang Graben" and walk along this street, the "Graben". Habsburgergasse is the fifth street on the left.
There is also a shuttle bus from the airport to Morzinplatz/Schwedenplatz. The journey takes about 20 minutes and costs € 8. From Schwedenplatz, take the underground line U1 in the direction of Reumannplatz to Stephansplatz station (1 stop). Once here, follow the signs to "Ausgang Graben" and walk along this street. Habsburgergasse is the fifth street on the left-hand side.
We will be happy to organise an airport pick-up/shuttle for you on request. The cost of the taxi journey (for up to 4 people) is € 48 to € 68.