The fastest option: Take an ÖBB regional train (REX/RJ/RJX) from the airport to Vienna main station (Wien Hauptbahnhof). They go approximately every half an hour and the duration of the drive is 17min. At the main station, take U1 (red metro line) in direction Leopoldau and get off at Wien Taubstummengasse (one stop). Then walk 140m to the hotel Johann Strauß at Favoritenstraße 12.
Buy the train ticket at the airport at the red ÖBB ticket machines close to the rails (costs 4,50€, select Wien Taubstummengasse). Do not buy tickets for the CAT train at the green CAT ticket machines, they are not valid in ÖBB trains and they are much more expensive. CAT trains do not stop at Wien Hauptbahnhof.
There are alternative routes to get to Wien Taubstummengasse (S7 train to Wien Praterstern and U1 in direction Oberlaa to Wien Taubstummengasse), check the ÖBB app or website for the current train schedule.
In case you arrive at the airport very ealy in the morning or very late in the evening and there are not many trains running, there is the option to take the buses of the Vienna airport line. Tickets can be purchased on the website or on board (costs 10,50€ one way, 17,50€ both ways). Line VAL1 goes to Vienna main station. Line VAL2 goes to Schwedenplatz. From Vienna main station (one stop in U1 direction Leopoldau) or Schwedenplatz (three stops in U1 direction Oberlaa) you can take U1 to Wien Taubstummengasse.
Take U1 (red metro line) in direction Leopoldau and get off at Wien Taubstummengasse (one stop). Then walk 140m to the hotel Johann Strauß at Favoritenstraße 12. Buy the metro ticket before entering the station at the ticket machines (costs 2,40€, select Wien Taubstummengasse).
Alternatively, the hotel is about 20 minutes walk (1.6 km) from the station, along the street Favoritenstraße.
Walk 600m from the hotel via Favoritenstraße and Wiedner Hauptstraße to the TU Wien main building at Karlsplatz 13. Alternatively, you can take the U1 from Wien Taubstummengasse in direction Leopoldau and get off at Wien Karlsplatz (one stop).
Directions to the exact rooms to be added later.