In July of 2010 I spent about 10 days in Vienna and fell in love!
I adored the food, culture, museums, galleries and pretty much everything else.
Best galley/museum was definitely the 'Albertina' which houses a great collection.
Sachertorte was a must at the Sacher Hotel - where else?
I found the metro system excellent and used it the whole time. We used a prebought ticket with which you just got on without any bother.
When we went it was averaging around 37 celsius so we were very lucky. Even if it meant our 'Manner' and ice cream got a bit melted!
The Reisenrad (Giant Ferris Wheel) was good fun and is definitely a must - try for a clear day though!