Former Summer Palace of the Habsburgs, Schönbrunn is on the UNESCO World Heritage list and is one of the most popular destinations in Vienna. Various tours are available of the Palace itself (priced from €13.30), but wandering around the gardens is free and well worthwhile, particularly the ten minute walk up the hill to the Gloriette, for great views across the city.
Getting there: By Tram #58 from just behind the hostel on Mariahilferstrasse, in front of Billa supermarket (6 stops, direction 'Unter St Veit'). Takes 5-10 minutes. If you don't already have a transport pass, buy a ticket on the tram for €2.30 (coins only). Walking takes 25 mins or so. To / From the city centre, take the U4 U-Bahn line ("Schönbrunn " station).