I was excited about eating my way through My Favourite Things (crisp apple strudels, schnitzel with noodles...) but a little daunted by recollections of my dad's trip to Frankfurt when he'd found very little to eat other than bread, and very little to drink other than beer. As it happened, I found more than enough to eat and love. However, I realized that local dishes which were inherently vegetarian were sometimes off menu or only available in a couple of restaurants, and I was glad I'd put in some compulsive research time before my trip. I'm going to save you some time and put down a list.
Brotchen: Bite sized open faced sandwiches with toppings you don't see anywhere else. I had onion and mushroom, carrot and cream cheese, and tomato chutney. The cost of these little things start to add up, but they make for a satisfying meal in between meals, and Trzesniewski is a Viennese institution.
Schnitzel: Usually made of tenderized meat, Vienna has several options made with tofu or TVP. I'm not usually a fan of food that's, essentially, processed, but in this case I'm willing to make an exception. The schnitzel at Landia in Vienna was a-ma-zing. I also went a little overboard and ordered their goulash with dumplings, another traditional dish which they veganized with great success.
Käsespätzle: Called 'little sparrow' since the hand shaped noodles resembled little birds, this pasta dish melds grated Emmenthaler cheese and fried onions in a pre-ordained love-match. There are other versions which include minced cauliflower which are equally good. Other cheese based pasta/noodle dishes are Kaspressknödel, and Kasnozk'n. You'll find nice versions at Andreas Hofer Steingasse in Salzburg.
Liptauer: I've told this story before, but Andreas Hofer Steingasse went out of their way to make me this traditional bread dish. It's a spicy spread made with sheep/goat's milk cheese mixed with sour cream, finely chopped spring onions, and some combination of flavours that make the whole thing sing. If you don't experience it in Salzburg, try the similar obatzda, served at most beer halls in Munich.
Currywurst: More commonly associated with other parts of Germany, Bergwolf in Munich nonetheless serves up an excellent vegetarianized version. This fast food dish consists of a full plate of fries (fake meat optional) seasoned with curry ketchup.
Special mention must be made of the Mozart balls in Salzburg, which, while commercial, taste like they deservedly won prizes (Cafe Furst has the best, though they're more expensive); butter brezel in Munich which is the only salted pretzel I actually like; schneeballs in Rothenburg which were the size of my head but well worth the calories; and the infamous sacher torte, a layered chocolate & apricot cake which turned out to be less dry than I'd feared.
Also - I should mention that I usually check out the McDonald's menu in every city I visit. It's a helpful index of prices and tastes. I was delighted to note Munich had the only vegetarian burger I've seen outside of India, and it honestly tasted incredibly good, way better than the McAloo Tikki. Clearly a lot has changed between the time my dad visited Frankfurt and now.
A full round-up of food reccos for Germany/Austria is here.