I was lucky enough to be in Vienna for 12 days in May for work and try almost everywhere I wanted (couldn't get to Steiereck, but I did have a great meal at Meierei). Chowhound was my main source and thanks to posters like Sturmi, I had a fantastic trip and some truly memorable food. I booked at all of these places and would recommend doing that. This is my belated report:
Figlmüller - a great way to start off a trip to Vienna, even if the standard schnitzel I had at their Wollzeile location was pork and therefore not a Wiener and not my preference. I loved the pepperiness of the potato salad and got a free glass of sparkling wine for showing my Austrian air boarding card. I was solo and had booked (you definitely need to, I saw as many people turned away as were eating!) and was happy to share the other seat at my table - a Swiss student was seated there and we had a chat about his taking a ferry from Vienna to Bratislava. Next time! I like the bustling atmosphere.
Phonixhof- lovely fritattensuppe, large rostbraten with crunchy onions and delicious potato wedges, and a fantastic dessert I've never had before: Germknödel, a fluffy yeast dough dumpling with a mix of poppy seeds and sugar, filled with plum jam and with melted butter on top.
Gaumenspiel - perhaps my favorite meal and certainly my favorite fine-dining one. Such friendly service and delicious asparagus ravioli with hollandaise and white asparagus, some orange/asparagus soup I didn't take a photo of, a lovely seabass filet with crayfish and fennel, and a tonka bean meringue tart for dessert - fantastic.
Glacisbeisel - perhaps my second-favorite place and definitely my favorite more casual one - I ate there twice! Beautiful outdoor seating, tucked away in the back of the Museum Quartier. I had asparagus (there's a theme here!) and Bauernschinken (farmer's ham) that took me back to the ham I had as a treat from the NYC German deli Schaller & Weber when I was growing up. There was a egg vinaigrette as a dressing. I had tafelspitz and it was delicious - a close second to Rudi's Beisl, but that is coming up. I liked the large amount and mix of veggies (yellow carrot, leek) and it's lighter than Rudi's Beisl's version. The crispy potato pancake that came with was amazing. Can't believe I managed dessert, but I had Topfenknödel, Curd cheese dumplings, with plum sauce. My second meal was an asparagus and strawberry salad - refreshing, although I am not convinced of the rightness of pairing asparagus with orange or strawberry - and Grammel-Knödel, or dumplings filled with pork crackling. I'm sure they were done well but too heavy for me, for once! I also had semolina flummerie, or pudding, with berry sauce - yum.
At Rudi's Beisl, I had more spargel (asparagus) with ham and hollandaise - lovely, and there was a choice of preparations. I had tafelspitz and the meat was amazingly tender, like my grandma's pot roast but better! The potato pancake was a tad greasy but still delicious. I skipped dessert and had it later at Cafe Sperl - plum cake and "grandma's coffee," which was milky and perfect for me. It's a little out of central Vienna but worth it - delicious, hearty, homey, unpretentious, and friendly.
Meierei - almost as good as Gaumenspiel. I had venison with hazelnut Schupfnudeln (like skinny gnocchi) and Japanese medlar (an apple-y fruit) and mushroom. Lovely, rich flavors brightened by the medlar, and for once, no grit on my mushrooms (I have bad luck with that even in fine-dining places). I then had a fantastic Kaiserschmarrn, chopped-up pancake with cherry sauce, fluffy and crispy.
Vestibül was my second dinner of the Meierei day so I only had a half-schnitzel there - veal this time and so good.
What to do on a Sunday when so many places are closed? There's Ilona Stüberl, which is central - I had a chicken stew with spaetzle, which was tasty enough, and their special choc-apricot palacinta (crepe) for dessert. The male waiter was a bit grumpy and unhelpful.
At Beim Czaak, an old-fashioned kind of place, I had the Fiaker goulash (comes with a fried egg, sausage, potatoes) and a dessert I recommend -Nougat knödel, which are only about 2 or 2.50 eur each and so good I am going to make it at home!
The only place that gets lots of praise that I liked less was Zum finsteren Stern. True, I ate at 9pm, but they were out of 2 dishes - a starter and main - and in such a small place with so few choices I thought that was careless. Then they brought me the wrong starter. I did have an interesting if in my mind unsuccessful orange crepe with asparagus (that pairing again - I was curious, but still unconvinced) and beef with fine beans and a salsa verde which was quite tasty, but fairly small. Perhaps they had an off
Now I'll have to seek out Austrian food in London. Luckily, there is a food truck dishing out some mean schnitzel and speckknödel - speckmobile!