On the first trip in Austria, in 2003, we came from north, passing by the lake. Spend one night at the 4-star Hotel Nordbahn in Vienna. We visit it all from Stephan Plaze towards Heldenplatz, Theresienplatz, Schmerlingplatz, Rathaus, Roosvelt platz.
Second & third times, on our way to the west, we stop in Vienna for an afternoon each time, but we choose to stroll up & down the main area, and use the rest of the time to dine at fancy restaurants.
Both times we follow the same route, south of Graz toward the italian border, stopping on the way a few times for shopping & dining.