Where did different human races come? How did each race end up in different locations around the world? Did God scatter races at Babel for a reason?
First, we recommend you read our article on the Bible's perspective on race.
Secondly, the Bible teaches that the scattering of humanity at Babel was exclusively a matter of confusing human language, not of race:
Gen. 11:7 “Come, let Us go down and there confuse their language, so that they will not understand one another’s speech.”
Gen. 11:8 So the Lord scattered them abroad from there over the face of the whole earth; and they stopped building the city.
There is no reason to believe the Lord separated mankind based on physical traits at Babel. On the contrary, human "races" resulted from the scattering. Mutation and natural selection within human DNA explain the expression of different physical traits between populations of human beings (i.e., "races"). The Lord designed diversity and adaptation into Adam's DNA, and the variation in human traits that cluster according to region or ethnicity is a result of normal genetic processes.
The Lord's scattering of humanity at Babel was the catalyst to trigger ethnic groupings, and a similar effect followed Noah's departure from the ark. For a more thorough explanation of the genetic consequences of the biblical events in Genesis, please read Noah and Genetics. We also recommend our Evolution vs. Creation seminar.
Regarding how people traveled from Babel to locations such as North America, see the following article in the Journal of Creation: The Ice Age as a mechanism for post-Flood dispersal.