Here are several ways to reach the Erste Campus by public transportation:
From Vienna Airport:
Train - our RECOMMENDATION
S7 or Railjet nonstop to Wien Hauptbahnhof. EUR 4,10 per direction.
Bus
There's also a bus "Flughafenbus Wien" from/to Vienna airport departing from Wien Hauptbahnhof.
Costs are EUR 13,- for both directions.
Public Transportation:
Underground U1
Tramway O, D and 18
Bus 13A, 69A
Trains S2, S3, S60, S80