First, distribution of ancestry in African Americans:
The higher fraction of African ancestry in the south and of European ancestry in the north, shouldn't be very surprising. There are some interesting loci of higher "Native American" ancestry; most African Americans don't seem to have a lot of this ancestry, but some apparently do.
Second, distribution of ancestry in "Latinos":
To my eye, this seems like more African ancestry in the eastern parts (presumbly from Caribbean-type Latinos?) and more Native American ancestry in the west.
Third, distribution of ancestry in European Americans:
Overall, it seems that relatively few (less than 5%) of European Americans have more than 2% either African or Native American ancestry in any of the states, so the breakdown of European ancestry into various subgroups is perhaps more interesting.
The distribution of African ancestry in European and African Americans is also interesting:
The existence of "African Americans" with virtually no African ancestry and of "European Americans" with as much as half African ancestry is probably due to either misreporting or some quite strange self-perception issues. The bulk of the African ancestry in European Americans seems to be in the sub-10% range (equivalent to less than 1 great grandparent). It is possible that many of these individuals might not even be aware of the existence of such ancestors.
bioRxiv doi: http://dx.doi.org/10.1101/009340
The genetic ancestry of African, Latino, and European Americans across the United States.
Katarzyna Bryc, Eric Durand, J Michael Macpherson, David Reich, Joanna Mountain
Over the past 500 years, North America has been the site of ongoing mixing of Native Americans, European settlers, and Africans brought largely by the Trans-Atlantic slave trade, shaping the early history of what became the United States. We studied the genetic ancestry of 5,269 self-described African Americans, 8,663 Latinos, and 148,789 European Americans who are 23andMe customers and show that the legacy of these historical interactions is visible in the genetic ancestry of present-day Americans. We document pervasive mixed ancestry and asymmetrical male and female ancestry contributions in all groups studied. We show that regional ancestry differences reflect historical events, such as early Spanish colonization, waves of immigration from many regions of Europe, and forced relocation of Native Americans within the US. This study sheds light on the fine-scale differences in ancestry within and across the United States, and informs our understanding of the relationship between racial and ethnic identities and genetic ancestry.