My number-two suggestion would then be Mraz & Sohn. It is situated where one would not expect a very fine restaurant (the Steirereck is also not quite central, by the way), but it is quite superb in many respects. Highly inventive cooking that generally works, excellent wine pairings available for all courses, cheeses in great profusion and perfect condition.
Coincidentally, I was at this restaurant for a business dinner earlier this week and would rate the best of those I have been to in several visits to Vienna. It tries a little too hard to be inventive at times (they served an after dinner treat of homemade cherry pudding in a pop top can), but still very good.