My husband and I were very comfortable at Pension Riedl in January 2004. It's just inside the ring at the Stubentor section - close to the metro stop on the U3 line and the Wein Mitte railway station where the new CAT train from the airport drops you. Consequently it's close to the main sights by foot, metro and tram. It's also right next to a traditional concert cafe and around the corner from a number of decent restaurants. The owner, Maria Felzer, is a very sweet and enthusiastic host, and speaks English. The rooms are clean, light, and comfortable.
Prices were lower than usual due to winter. We'd certainly recommend it.