Fortunately, Vienna International Airport (VIE) is not far at all from the city centre and there’s a number of different ways of getting into the city.
The CAT train will take you into Wien-Mitte centre in around 15 minutes. It costs somewhere in the region of €10 and operates from 05.30 to 23.30.
A cheaper but slower option into Wien-Mitte station is to get line 907 of the S-Bahn. It takes around 25 minutes and a ticket costs around €4. It runs from 04:30 to 00.15.
Alternatively, you can catch the Postbus coach which has approximately two departures per hour from 05.00 to 23.15. There are two routes, arriving at Morzinplatz/Schwedenplatz or Südbahnhof/Westbahnhof. A single journey will set you back around €6.
A taxi from the airport into the centre will take you around 20 minutes. Ordering one in advance can save you money. The journey should cost somewhere in the region of €30.
Finally, companies such as Ryanair often fly to Bratislava instead of Vienna International, so check your arrival airport to plan accordingly and avoid any surprises.