S2 train station is located near the first terminal. Follow the signs for the S2 train station. The train leaves every 20 minutes. One trip costs about five euros. The journey takes about half an hour. There is also a direct train from the airport to the city, the ticket costs twice as much, the duration of the journey is twice as fast. The direct train is green colored and easy to recognize by the gray-green CAT logo (City Airport Train). You need to go to the Vienna Mitte stop.
Photo: By Linie29 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=49097731
The Wien Mitte train station is the central hub connecting the train lines S-Bahn with a metro train system named U-Bahn. Look for U Bahn signs leading to the Landstrasse U-Bahn Station. Look for the ticketing machine to purchase the ticket. U-Bahn tickets are as follows: Day Ticket Vienna is valid on all public transport services in Vienna for one day from the started date until 1.00 am on the following day. (5.80 euros) 24-h Vienna ticket is valid on all public transport services in Vienna for 24 hours from the stated date and time. (8 euros) There are a variety of tickets, including the 48 and 72 hours tickets, weekly card and so else all are available at the ticketing machine.
Photo Von Gugerell - Eigenes Werk, CC0, https://commons.wikimedia.org/w/index.php?curid=26451702
Station Landstrasse, served by lines U3 and U4, is the large transfer station. Take the U4 line to the Hütteldorf direction. From the Landstraße stop, pass over the Stadtpark stop and exit at Karlsplatz stop. The Vienna U-Bahn operates daily between 5 am and 12:30 am.
By User:My Friend - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=5020437
The Karlsplatz square is one of the famous in the city. Its name comes from the Karlskirche located in front of a water pool with a sculpture by Henry Moore. The Karlskirche, with the building of the Vienna Museum (formerly the Historical Museum of Vienna), located to the east of the square. Photo of U-Bahn station Karlplatz By Manfred Werner - Tsui - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=5277078 Photo of Karlskirche By Wizzard - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=3112108