... is another well-established Cafe-Konditorei in Innsbruck (the oldest in Innsbruck/Tyrol). Konditorei means pastry shop and you can expect self-made cakes and pastries.
The Munding can be found in the old part of the town, leaving the Golden Roof behind you, heading to the Maria-Theresien-street, the last little street of the Old Town will lead you to the Munding square and the Munding cafe.
Everybody knows the famous Sacher café in Vienna - which also opened an outlet in Innsbruck in 1999. Locals like the Sacher breakfast for special occasions, tourists will go there to try the famous Sacher cake (which I personally do not think is sooo special - but find out yourself!).
Situated in the heart of Innsbruck, very close to the Golden Roof, the café Katzung is a place where people come and go, and come and go. The premises have been renovated in 2002. Try the Katzung cake, it's my favourite :-)
Austria is famous for it's coffee culture - the nice cafés where you can sit for hours and hours, reading newspapers, having a talk with friends or enjoy a nice cake along with the coffee of your choice. Vienna is famous for cafés like Sacher, Demel, Hawelka, etc. Innsbruck is the small version and there are some places worth to experience - especially after a tiring sightseeing or shopping :-)
I am not used to drinking carbonated water, but it's a very big thing in Europe I guess.
So if you don't want to end up with seltzer-type water, ask for "water without gas"...otherwise if you just ask for water, you will get bubbles.
in the grocery stores, you have to look carefully to notice if you are buying bubbled water.
If you like beer try weissbier (sounds like "vice" beer). It is made from wheat. The beer has a cloudy, white-ish appearance. Tastes great and very hard to find back in the states.