Besides the Schönbrunn Castle the Hofburg is for sure the most famous tourist attraction of Vienna. I recommend to take a walk from the Museumsquartier to the Michaelerkirche - on your 1-2km walk you pass the Natur- and Kunsthistorisches Museum, the Heldenplatz, Nationalbibliothek and finally go through the Hofburg to arrive via Spanischer Hofreitschule at Michaelerkirche . The nicest 2 km in town for sure.