Why Didn't the Germans Bomb Big Ben During WWII?

Short answer: They tried but luck intervened. 

Quora has a longer take on the mechanics of WWII bombing.  The rub:

At the time of the Blitz, the Germans, like every air power, did not have the ability to specifically target key buildings through high-altitude bombing raids, which were themselves necessary to hit valuable targets in order to avoid intense anti-aircraft fire. That combination of factors resulted in the reliance on city-flattening, strategic bombing raids: Just drop a bunch of bombs from where the guys on the ground can't hit you and hope for the best.