Don't let me dissuade you from a visit to the Bräunerhof! I didn't want to imply that their pastries are sub-par, and I think the atmosphere is pretty much unique. But if it's pastries first and foremost, I suggest Demel or Landtmann. Both have "atmosphere", too, but expect lots and lots of tourists (not a bad thing per se, of course). As to fine dining, I have heard that Steirereck is firing on all cylinders again, but haven't been there for a long time. I have had some excellent meals at the "Le Ciel" restaurant in the Grand Hotel over the past few months. Highly recommended. If this link works, it should give you an idea what to expect. They are very much into unusual herbs and spices. http://www.leciel.at/index.php?idp=4〈=2