This is by far one of my most favorite weird spots in Munich. Once you are at Marienplatz (the city center of Munich), stand in front of the Neues Rathaus. Now go the left corner of the building and look up.
You will see a large figure of a green dragon, positioned on the Rathaus. If you paid attention to Marienplatz, you might have already noticed that there is also a small dragon being killed by an angel at the obelisk in the center of Marienplatz. In the middle ages in Bavaria, the dragon was often the symbol of hunger.
It is one of the many status there so make sure to look around for more.
Once you are done, have a look at the mechanical clock. The Town Hall is famous for the mechanical clock (Glockenspiel) which is a carillon with 32 life-size figures that go round and dance with music for about 15 minutes.