Climb the 165 steps to the top of this fortification tower that was inhabited by a sentry until 1904. En route, exhibits on the purpose of such sentries (eg keeping an eye out for fire or advancing marauders) provide a modest excuse to catch your breath.
There's another tower a short walk south of here on Marienplatz, called Dicker Turm (Fat Tower), thanks to its 6m-thick walls.