Google is an amazing research. In the film, it is mentioned that they were in Vienna. But that doesn't mean that they really film in Vienna. Fortunately for me, they did film in Vienna! Well, that information is on the Wikipedia page. But how to find where is the city this one specific shot was filmed at? I took Google again and search for "The Third Man locations." I discovered that there are The Third Man super fans that travel to various cities in search for film locations.
Turns out that building with the shadow is part of a wing of the Hofburg called Stallburg. The Hofburg is actually located in the center of Vienna and was built in the 13th century for Roman Emperors. Currently, the Hofburg is used for the secretaries of state, Federal President, and the ministers of the chancellor's office. The statues that are seen in the corner of the frame are part of a fountain called Power on Land.
I know everything in the scene is small going to be small in frame, but with the awesome power of Google Maps, I can see all the finer details needed for modeling. I can move in all directions and look around. I took screenshots to better understanding of how the street is layed out. Vienna is an old city and not much has changed since the films release other than a few store updates.