I have stayed at three hotels in Vienna, all of which I would recommend. Nearest to the Staatsoper of these was the Pension Residenz, Ebendorferstrasse 10
A-1010 Wien, Österreich
Telefon: +43/1/406 47 86 0
Fax: +43/1/406 47 86 50
rooms 70 or 80 euros for a single, including breakfast.
This is just off the Ringstrasse near the Rathaus and the University, about 20 minutes walk or a very quick tram ride to the Staatsoper.
A little further away is the Pension Excellence, single rooms starting at 61 euros including breakfast buffet. On the second floor they also have apartments complete with kitchenettes which you can stock from the nearby Billa grocery store, Vienna Comfort Apartments, starting at 97 euros per night, breakfast 9 euros extra per person. This is closer to the Volksoper if your ballet performance happens to be there. You can walk to the Staatsoper in about 25 minutes, but tram service is also excellent.
The Gartenhotel Gabriel, Landstrasser Hauptstrasse 165, 1030 Vienna, Austria, Tel.: +43 1 712 32 05,
single rooms starting at 47 euros including a great breakfast buffet, is not within walking distance of the theatre but is on a tram line with frequent service that will get you there in 10 minutes. Its great advantage in addition to the budget price is that it is very close to the Sanct-Marx S-Bahn station for the airport train, which is very helpful if you have to catch an early flight.
There are so many fabulous cafes in Vienna that it's impossible to list them all but my favourites include:
Cafe Central for its sheer beauty
Heiner Wollzeile 9, 1010 Wien: This is my all time favourite, possibly the best cakes I've ever eaten in a truly "gemuetlich" atmosphere. There are other Heiners, particularly one on the busy Karntnerstrasse pedestrian street, where the cake is equally good, but as this one is slightly off the tourist beaten path and doesn't seem to be listed in the guidebooks, you will find yourself in the company of Viennese people and families who have just popped in for their fix of coffee and cake. It also offers nice light lunches. While you're there, head down the street and around the corner and check out the Jesuitenkirche, which will blow your mind with its baroque extravagance.
Demel just down from the Hofburg is overrun with tourists but you just have to go there for your Viennese experience to be complete, and the cakes are wonderful.
Cafe Schwarzenberg not far along the ring from the Opera House at Schwarzenbergplatz (the terminus of the tram from the Gartenhotel Gabriel) is a good place for an inexpensive dinner of classic Austrian cuisine before a performance. The cafe at the opera house itself also offers inexpensive light meals.
After the show, if you find you need even more cake, it may be hard to find places open, but the Cafe Mozart (it really has been there since Mozart's time) in Albertinaplatz opposite the back of the opera house is open till midnight.
When you go to visit Schonbrunn castle, the Oberlaa cafe in Hiezing is very pleasant.
If by now you think I have eaten cake in every cafe in Vienna, you are probably right!