Take the Ringstrasse on one of the streetcars and you'll get the layout figured out from the start.
The Osterreichische Galerie Belvedere is a museum in the Belvedere palace that is well worth seeing.
Kunst Historisches Museum is not to be missed if you love fine art.
Schönbrunn Palace was the Habsburgs' summer home and is another place I wouldn't miss.
Overall, Vienna is a wonderful city that is right up there with London, Paris or Berlin for museums, palaces, art and of course music. Enjoy!!!