I noted this article awhile ago, but just didn't get around to posting it here until now.
The gist is that traditional stats have a limited view of what counts as an immigrant household, such as whether the head-of-household is an immigrant. This count is no good because it would exclude a household where a US-citizen head of household marries an immigrant. Go ahead and read it, it's not long.
So, check out the map graphic and the caption. The bottom map includes households with kids and grandkids of immigrants and suddenly the whole country looks more diverse.
Except the Deep South. Yeah, I know, stereotypically, these are the redneck states, insert your joke here. But seriously, that cluster has the only dark blue states on that map. Alaska has a higher percentage of immigrants (though most of its population is in big cities so maybe that makes sense). But what about North Dakota? Montana? There's nothing there! Why would immigrants go there?! The Deep South has agriculture, and population centers. Why is the immigrant percentage so low? Does this support the notion that the South is not friendly to outsiders?