The Wien Museum is free on Sundays (which is a nice discount from the normal 6 euros). It was really interesting to see the changes of Vienna from the Roman occupation to the Hungarian Empire and then the modern day occupation. It has city maps, old plans and statues rescued from renovated buildings.
There is a special exhibition currently hosted at the museum showcasing Vienna in film. Its quite interesting to see the depiction of Vienna after seeing the city.
The Karlsplatz Kirche is currently under construction but beautiful nonetheless. The pillars framing the church entrance are carved with complex scenes. There is rumoured (we of limited funds did not pay the massive entrance fee) to be a massive fresco on the ceiling covering roughly 13500 feet.