Is American culture Euro-African-Mexican mixed?

In the picture above it shows the regional variations of American culture based on original colonial clusters on the eastern seaboard and their migrations west.

Yankeedom's culture has its roots in English Puritanism. New Netherlands is a multicultural society with origins in the Netherlands with many ethnic groups such as Jews, Greeks, Italians, Irish, and various other cultures which have kind of kept their identity. The Midlands cultural origins lie in English Quakerism and German immigrants. Greater Appalachia has its origins in Ulster Scots from Northern Ireland. Tidewater has its origins in southern England and was founded as a feudal aristocracy led by Cavaliers fleeing the English Civil War. The Deep South where I'm from has its origins in the English Caribbean slave state of Barbados; it has two cultures African American culture and a very conservative southern white culture with roots again in southern England. The New France part of Louisiana has a culture which comes from French Acadians that were expelled from Canada and blacks and whites from the French Caribbean. El Norte is a northern Mexican culture that differs from the other parts of the country as being more Americanized with origins in Spain and Native Americans. The far west is kind of a libertarian cowboy type culture, and the Left Coast is the western extension of Puritanism mixed with Appalachian individualism.

To answer your question, there are many variations of American culture which stem from various religious groups, aristocrats, and money making ventures in Europe. It should be noted that the areas labeled Deep South, Tidewater, Greater Appalachia, and New France have since the Civil War and reconstruction and even before consolidated under one cultural identity called the South. They differ very little having a common working class redneck culture, a social conservatism which puts anything you find in Europe to shame, a common southern baptist evangelical faith, common music, common speech patterns, a culture of honor and masculinity in which insulting some one could get you beaten up horribly, a distrust for the federal government and a tendency to want a small federal government and more powerful local government, a focus on their large extended families, southern hospitality and politeness, and a very stubborn and prideful attitude which does not take into account what what anyone thinks of them and their history, and a love for their guns, bibles, and constitution. I am proud to be a southerner. 

I'm not sure how I feel about New Mexico being a part of Appalachia

Okay so basically Barbados was an island in the Caribbean settled by Englishmen. Being a volcanic island it was very very fertile. When sugarcane became the most valuable resource in Europe the Englishmen imported boatloads of African slaves and worked them to death in sugar plantations because they could afford to just buy more slaves to replace the dead ones. Eventually a fabulously wealthy aristocracy of plantation owners developed on the island descended in large part from Cavaliers in England who made their money in sugarcane.

Eventually these plantation owners ran out of land on the island to give to their sons and sought new land in the Caribbean and then eventually on the North American continent. The colony of South Carolina was called Carolina in ye West Indies and a colony of a colony because starting from the coast it was settled by plantation owners from Barbados and their African slaves which the brought with them to grow rice instead of sugar.

Eventually the plantation owners expanded into coastal Georgia as well and then when the cotton gin was invented they spread through the subtropical lowlands into Alabama, Mississippi, North Louisiana, east Texas, and Florida, and everything else you see on that map labled Deep South.

The Deep South was a culture built upon slavery and racism sadly. The plantation owners revered the slave states of Greece and Rome and their type of republic where democracy was the privilege of a cultivated and enlightened aristocracy and enslavement was the natural lot of many people. Society was structured into three classes, the plantation aristocracy who ran everything and were large landowners, the poor whites who were Yeoman farmers or herders who owned few slaves, and black people of whom most were slaves and were not even considered human beings.

The society of the deep south was basically rural, agrarian, feudal, aristocratic, white supremecist, caste based, extremely conservative and reactionary, religious, honor based (disrespect by one's equal usually led to a duel), patriarchal, and based entirely on the institution of Negro slavery.

When Abraham Lincoln was elected president the first seven states to secede from the Union were all of the states run by the Deep South and the very first to do so was the state of South Carolina my home state.

Now you may ask why I am proud of being from a place with such a dark legacy? Well because of my regions origins as a reactionary feudal aristocracy we have inherited some great traditional European values that have been very resistant to the radical left. My region votes like an ethnic block against the democrats and remains religiously fundamentalist and extremely socially conservative and retain traditional European values far better than any society on earth.