(There is a hidden spot on this picture.)
Stefansdom is the virtual, if not the geographic, center of Vienna's Altstadt.  This picture shows a model of the "original" city, and you will see that Old Vienna can be honestly described as "St Steven's surrounded by miscellaneous buildings".
The building is covered with odd little details the casual observer will miss.  Luckily, we had as our guide an Austrian who has lived here for many years, and he pointed out a few of them to us.  You can't see it in this picture, but scratched into the masonry near the main door is a large "05", a secret symbol of the Austrian resistance.  In German, "Austria" is "Österreich".  O-umlaut is otherwise written as "Oe", and this was transliterated as 'zero-five' because 'e' is the fifth letter of the alphabet.
Architecturally, Stefansdom is crazily unbalanced.  The apse tower visible in this picture is not matched by a similar tower on the other side.  It is said that they ran out of money during construction and left it unfinished.  That may or may not be true... Austria is and always has been very Catholic and the church simply does not "run out of money", so there may be an alternative explanation.