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).
Vienna is famous for it's old style Coffee-Houses. Along the way, try to find some famous one's like '''Cafe Central''', '''Cafe Demel''' and '''Cafe Hawelka''', they're all around the downtown area near the '''Kaernter Strasse'''.
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.