Something a bit special: An apartment building designed by the fascinating Austrian artist Friedensreich Hundertwasser, with an emphasis on bold colours, the incorporation of nature, and a rejection of straight lines. There are strong similarities to some of the Gaudi buildings you might've seen in Barcelona. If you like this, check out the nearby 'Kunsthaus' (a few blocks over), also designed by Hundertwasser.
Getting there: From the hostel, take the U3 U-Bahn line from Westbahnhof (direction 'Simmering') to Volkstheater. Change to tram 1 (direction 'Prater Hauptallee') and get off at Hetzgasse. Takes about 30 minutes.