I had a couple of good meals while I was in Vienna. The place I liked the most, in terms of atmosphere and cuisine was Amerlingbeisl. It had a fantastic courtyard seating area with a really beautiful arbor of hops (or some such vine). It was quiet and charming. The waitress was really nice and recommended a great glass of wine with the meal: asparagus wrapped in a farmers ham, and spuds swimming in butter( hell, I'd bet the potatoes were marinaded in butter the night before).
The best part is that this is all squirreled away in a two story Biedermeier style building in the heart of Vienna (probably from the early 1800s or late 1700s). The building also serves as a cultural center for the Spittelberg neighborhood. But the cultural center was a product of the 1970s, not the 1800s. Check out the pictures from the 1970s. Check out the courtyard panorama on the restaurant's home page too.