The Tower of Babel definitely existed in Babylon. The Greek
historian Herodotus wrote of the ziggurat. Even in 460 BC, after
the tower had been crumbling for many years, the Greek historian
Herodotus visited the tower and was very impressed. "It has a solid
central tower, one furlong square, with a second erected on top of
it and then a third, and so on up to eight. All eight towers can be
climbed by a spiral way running around the outside, and about
halfway up there are seats for those who make the journey to rest
on."
There are three possible locations for it:-
...[T]he Tower of Babel [is] somewhere in Babylon [b]ut there
are three principal opinions as to its precise position in the
city.
(1) ....located the tower in the north of the city, on the left
bank of the Euphrates, where now lie the ruins called
Babil.......
(2) ... places the tower on the ruins of Tell-Amram, ...These
ruins are situated on the same side of the Euphrates as those of
the Babil, and also within the ancient city limits.
(3)...tower of Babel with the ruins of the Birs-Nimrud, in
Borsippa, situated on the right side of the Euphrates, some seven
or eight miles from the ruins of the city proper. ...