We had a marvelous time in both Vienna and Salzburg, and ate lots of delicious food. Nothing that was particularly high end, we preferred traditional beisl and cafes for the most part. I got many good suggestions here, hoping to pay it back a bit with a report.
Our hotel in Vienna was the Maria Theresa, between the Museum Quartier and Spittleberg, so most of our dinners were in that area.
Glacis Beisl -- Right across the street from our hotel, couldn't be more convenient, and this was the best meal of our trip. We had wild garlic soup which was different than I expected and incredibly delicious. I had the tafelspitz, which was flavorful, slice boiled beef served with carrots and leeks, home fries, sour cream and chive, apple chutney with horseradish. The beef is more like pot roast than anything else, but better. And the fresh horseradish and apple is really good. My companion had the asparagus with ham and hollandaise. I've had white asparagus at home, and I don't care for it...but the thick stalks of Marshfield asparagus we got in Vienna were incredibly good. it became a theme for our week, since it was in season, we ate asparagus every chance we got. We tried to get a reservation on Saturday afternoon for Saturday night and couldn't...we did manage to get a table as a walkin, but I wouldn't recommend it. We got the last free table, and people after us were turned away. This was at 7PM.
Boheme -- this is on Spittleberg, on the corner. We didn't have a reservation so couldn't get an outside table, but it was fine inside. The restaurant was recommended by the hotel staff, and reading reviews on tripadvisor, I suspect they have an arrangement with lots of hotels. That said, the food was very good. We tried the schnitzel here for the first time, and it was excellent. I had grilled chicken with the ubiquitous white asparagus and hollandaise, and loved it.
Amerling Beisl -- this was pretty good, but maybe not as good as the other 2. The menu had fewer choices, and service was very slow. But I had fish filets, served with spinach and mornay sauce, and enjoyed it.
Cafe Demel -- we had lunch here. I figured it was a tourist trap and didn't expect the food to be that good, but I was mistaken. I actually had a thoroughly fantastic quiche lorraine. And dessert of course...I had an interesting ice cream concoction with coffee ice cream, and sour cherries and whipped cream. My companion had the truffle torte...definitely the best of the various chocolate cakes that we tried.
Cafe Sacher -- we had a very nice late lunch here. Fried chicken, potato salad and of course, sacher torte. I've decided that the Viennese potato salad with bacon, and oil (no mayonnaise!) is one of my new favorite foods. And yes, the original sacher torte is kind of dry, and doesn't have enough jam flavor. But its a nice place, and a little dressier than the other cafes.
Cafe Museum -- another really good lunch. We tried asparagus cordon bleu here. They wrap the asparagus with cheese and ham, then breadcrumbs, and deep fry. It's served with tarter sauce, which is lighter and better than the stuff we call tarter sauce in the US. Yes, this dish is as decadent and delicious as it sounds.
Konditorei Oberlaa -- this is about a block or 2 from the Albertina. I mention it because it had the best ice cream of the trip. A great place to stop for a snack on an 80 degree day (which we had a lot of...who knew it would be 80-85 and sunny every day, the first week in May???)
Okay, that covers most of the highlights of Vienna. Will come back and add Salzburg in a reply...