The tower of Babel would have been located in the plain of Shinar, Nimrod (son of Cush, son of Ham) probably orchestrated its construction.
The attitude, both expressed and perceived, was very prideful. Those involved were seeking to be the masters of their own destinies. The Godhead perceived their intent perfectly and they conversed amongst themselves: "nothing will be restrained from them, which they have imagined to do." Humanism is not a new philosophy. "Can we do it? Yes, we can!" Sounds familiar, huh?
So God confounded their languages. As I read this account, I can't help but wonder if God's about to confound the money of the world system--the U.s. especially--for the same reason, but that's beside the point. When God did confound their languages, the event brought they proud progress to a grinding halt, and the project was forgotten in the wake of the new crisis.
The imagination can go wild in this scenario. We're not given many specifics, but it will be interesting to have perfect knowledge of this event someday in heaven. In the meantime, I can note, after carefully mapping out the generations, that the account of occurred between 102 years and 341 years after the flood. I tend to lean in the 102 year direction, as Peleg's meaning implies division. If Peleg was born and given his name because of the division of languages, the tower incident would have been 102 years after the flood. This timing would also be about right for Nimrod's generation (fourth from Noah) to be doing the building.