In a pinch there is Haas:http://www.haas-haas.at/
It is right in the center of town on the back of the cathedral.
Their tea buyer there is quite friendly! She was patient and engaging. Happy to talk about tea. Is the place a super intense gung-fu kind of place? Of course not. But if you go in the back there is a small lovely garden patio where you can have food and brew, all in the shadow of Stephansdom. They had some korean boseong.
If you go there, be sure to stop in and say 'Hi' to Ludwig at Vinotek. They have some great Scotch, wine and other spirits.
I also bumped into another decent looking tea shop a few blocks away from Domplatz. It is called Schönbichler, on the corner of Wollzeile and Essiggasse. It looked pretty Mariage Frères style. There I bought 50 g of Szechuan black and they threw in a free sample.