Standing at Marienplatz, in front of the city hall "Rathaus" you find yourself right in the heart of old town Munich. The facade of the Rathaus is gigantic - take care though: the appearance is misleading. The Rathaus was not built in the middle ages as it might seem, but in the late 19th century - one example of German "Gründerzeit style", a historical backdating style - around 1900 people apparently did not want to fully endorse the new techniques that science and industry had brought around but built houses that looked like castles or temples.
Just around the corner is Frauenkirche, though. That is a real piece of medieval architecture and a very dominant one. You will not easily forget your eyes sweeing up those dwindling twin towers. Frauenkirche is probably the best known symbol of Munich. You might want to step inside - right at the entrance is a bizarre example of a tomb monument for a Habsburgian ruler. Frauenkirche is gigantic but has a "romanic" touch that sets it apart from the high spires of late gothic domes like the one in Cologne. You might want to climb the stairs for a view over munich and to the alpian mountains (only when there is "Fön", i.e. a wind coming from down south Italy and clearing up the northern Germanic skies).
If you care for some even more enthusiasm in the field of art and religion go for the Asamkirche, 200 m further south. That is Bavarian baroque on its peak.
Links refering to further information about the Munich Frauenkirche can you find here.