The Weltzeituhr is the 16-ton world clock on Alexanderplatz, built in 1969 and still used as one of Berlin's most reliable meeting points. Its rotating cylinder lists cities around the world by time zone, a neat piece of East German public design in the middle of the square.
It is not a destination by itself, but you will almost certainly pass it while crossing Alexanderplatz. Stop for a minute and the Cold War-era optimism of the thing becomes part of the scene.