In Genesis 11:1-4, we are introduced to the descendants of Noah after the flood:
1 And the whole earth was of one language, and of one speech.
2 And it came to pass, as they journeyed from the east, that they found a plain in the land of Shinar; and they dwelt there.
3 And they said one to another, Go to, let us make brick, and burn them thoroughly. And they had brick for stone, and slime had they for morter.
4 And they said, Go to, let us build us a city and a tower, whose top may reach unto heaven; and let us make us a name, lest we be scattered abroad upon the face of the whole earth.
Back in Genesis 9, God blessed Noah and his three sons (Shem, Ham and Japheth) and told them to be fruitful, multiply and replenish the earth. Then God establishes a covenant with them (and their perpetual generations, which includes us) that He would never destroy all flesh with the waters of a flood and a flood would never destroy the whole earth again. Because God is not a liar, this covenant is still active.
On top of that, God made the rainbow the token of this everlasting covenant. It is not a coincidence that this important token of God's covenant has been taken and corrupted by the LGBT community as its symbol since the late 1970's.
Back to the inhabitants of Babel in Genesis 11:1-4. Notice how they dwelt in a plain in the Land of Shinar (present-day Iraq, just south of Baghdad). This is part of the area known by archeologists as the "Fertile Crescent" and the rivers and plains would be a natural draw to any nomadic people looking to settle down. Instead of continuing to go and replenish the earth, this group of people stayed put and decided to build and city and a tower. Similar to Lot in Genesis 13:10, they chose the well-watered plain that appealed to the flesh versus following the instructions of God to completion.