There is archaeological evidence that suggests the Tower of Babel did really exist in Babylon.The remains of the tower found in the dig site suggest it was actually an ancient Babylonian temple known as a 'ziggurat'.
The real Tower of Babylon
Although the Biblical story suggests that the Tower was a construction destroyed by God, historians think that the original Tower was a temple built in the 6th century BC called Etemenanki.
Rather than being destroyed through an inability to communicate and cooperate due to linguistic differences inflicted by God, the original tower was likely destroyed by an invading army.
Where did the Tower of Babylon go then?
Subsequent rulers of the area (including Alexander the Great) knocked down towers built at the site of the original tower, with the intention of constructing their own monolithic buildings in their honour.
Unfortunately, the area kept getting conquered by different invaders - and no one ruler managed to stay in power (or alive) long enough to rebuild the tower in all its former glory.