When I went to Vienna a few years ago I stayed in a hotel run by a family who owns 4 hotels in Vienna, many of them well reviewed. I enjoyed my stay and the service/rooms/breakfasts were lovely.
The family is named Pertschy. I stayed in the Pension Christina, but they have 4 hotels in the region. I believe the Pension Pertschy is the most ideally located.

Their website is : http://www.pertschy.com

Also I would recommend one of the tours I went on where they take you to dinner and then to a Mozart concert with the Mozart Orchestra. It was pretty touristy but the music was wonderful and I'm picky because I am a musician myself. I was very pleased with the caliber of the orchestra and the opera soloists who performed with them. The orchestra dresses in period clothes & wigs and is in a wonderful theatre.
This was advertised in the usual tour books, you could work with the hotel to schedule it.

Enjoy and have some Sacher torte for me at the Hotel Sacher!