Situated across from the Opera House and caddy-corner to the Albertina, I'd been meaning to visit…read morethis place for a thousand years. They have a very interesting store front, with a vast assortment of dried teas, accompanied by ornaments and tchotchkes in the windows.
Come to find out, Jäger Tee is Vienna's oldest tea shop (150 years!), and a very classy place. Its staff know tea inside and out, if that's possible, and can answer any question you could possibly have about their products, or tea in general. The shop has actually been in the family since its creation, which is pretty cool.
The place itself is cozy and quaint, and a site to be appreciated in and of itself. There is even a charming, albeit small, tea room in the back of the shop.
Not only will you be hard-pressed to find a place with a better tea selection in Vienna, but this place also sells some AMAZING shortbread cookies that are also made with tea! And this summer they had an iced matcha tea (green tea), that was liked by pretty much everyone at the Elite event (even people who normally don't like matcha tea, green tea in general, or iced tea!)
Finally, while it might seem a bit pricey, for the quality of the products and given the fact that you probably can't find most of the teas at other shops in Vienna, the prices seem completely reasonable, particularly given the helpfulness and knowledge of the staff.
I'll definitely return to Jäger Tee.