Ben Blatt at Slate had a great series of maps a few days ago highlighting language use in various states, focusing on what non-English (or non-English and non-Spanish) languages were most prevalent. Yesterday, Reddit user delugetheory took a similar approach to states' ethnic makeups, and the results are pretty interesting (see above).
New Mexico, Hawaii, and DC are the only states (or quasi-states, in DC's case) where non-Hispanic whites form the second largest group; Hawaii is plurality Asian-American, New Mexico is plurality Hispanic, and DC is majority black. Interestingly, while there are only a handful of US states where Native Americans form the second largest group, most Canadian provinces count First Nations, Inuit, and Métis people as their second largest ethnic group. That's not true of the big three provinces population-wise (Ontario, British Columbia, and Quebec) but it's still fairly striking.