It's pretty tough to find a starting point for something like Vienna, but start with the '''Hofburg'''(2), '''Heldenplatz''', '''Volksgarten'''(3), '''Parlament'''(4) and '''Rathaus'''(5) in the illustration. You can rent a horse-drawn carriage (called a "fiaker") to do this section of Vienna in style, and to save your feet.
Afterwards, head to the '''Opera House''' and take a look inside (you won't get tickets here, that would be beyond lucky), .
and then Then head up the '''Kaernter Strasse''' (the pedestrian mall) towards '''St. Stephens cathedral'''. Along the way you come by '''Hotel Sacher''', take a look at the pastries there (and their world famous cake - Sachertorte).
If you head further up north past the cathedral, you'll eventually will wind up at the '''Prater''', a very old amusement park with a big ferris wheel. If you ever seen the movie '''The Third Man''' with Orson Welles, this will look familiar. Take a loop with the ferris wheel to get a look across Vienna, and take a gander through the park.