Many thanks to Sturmi for his recommendations. Vienna is a magnificent, grand city. Stayed at the Ritz Carlton - perfection. This is where we ended up for our dinners:
Rudi's Beisl - Excellent, casual, traditional Viennese cuisine. In a residential neighborhood and mostly locals. That's what I loved about it. Really nice to sit outside.
Gasthaus Wolf - Excellent as well. Viennese cuisine, but in more modern way. Also is a lovely residential area - only locals. Service was lovely. Sit outside if possible.
I had Wiener Schnitzel at both restaurants and they were sublime.
Vestibul (This wss not high on Sturmi's list). It was good, but it wouldn't be my first choice. Expensive. The ambiance is very nice.