The Magical United States
The US is not a utopia of magicals living harmoniously with non-magicals. They don't have it all figured out and they are not technomancers nor do they have schools which makes more sense than Hogwarts (see Magical Education).
Unlike most countries in Europe, where for the most part the magical side runs parallel to the non-magical side (for example, magical UK occupies the same political boundaries as the non-magical UK), the magical US is not one country being run by one government.
The magical population is small, this is true world-wide so they cannot occupy the entire North America, even the part that belongs to the US. It's not possible, even with magic. Instead, the US is made up of independent enclaves, some as small as villages to as large as several states that trade, and sometimes even war, with each other. These magical enclaves are formed either because of similar cultures, similar ideologies, similar ethnicities or similar magical traditions (or any combination of the above).
Most of the magicals who immigrated to the US did so to escape Europe. The English magicals left the UK to escape the pure-blood agenda much like the Puritans left the UK because of religious persecution. Other people also left Europe to colonize what would be known as the US for different reasons: finding their fortune, escaping religious/political/cultural persecution, etc. There are more magicals in the US but they are spread out and they definitely aren't united. And some of these enclaves don't even occupy one territory but are spread out (see the Republic of Roanoke and Croatan).
Unlike their non-magical counterparts, the European wizards found a strong magical race that resisted their entry and while their non-magical counterparts successfully colonized the Eastern United States, the magicals had to fight the natives for every bit of territory.
Blaine's family live in the Republic of Roanoke and Croatan, which is more or less comprised of the New England states and some parts of upstate New York, as well as the cities of San Francisco and Seattle and Greenwich Village. They have their own version of the Wizengamot but it's split into two parts: the Caucus, which is the legislative branch, and the Justices, which is the judiciary. There is an executive branch but it's not presided by a single individual but by a tribunal.
Counting little villages and isolated communites (think Children of the Corn and the Texas Chainsaw Massacre), there are hundreds of enclaves all over the US. Each with their own way of running things, each with their own magical traditions. The only thing everyone agrees on is the Statute of Secrecy.
The Pure-blood Agenda, while it exists in the Republic, is a small, quiet minority. This is because most of the settlers left England precisely to get away from it so the majority of the people who are in the Republic are the ones who don't agree with it. The "purity" of blood is not what matters but how rich the family is and how long they have been in the Republic. The Andersons are considered an elite family because they were in the second wave of immigrants to what was then the "colonies" and because there are members of that family who have been outstanding statesmen, educators and so on.
While there is a bit of condescension felt towards non-magicals, there is also a healthy fear of them as well. Unlike the English Pure-bloods, their American counterparts are well aware what a "Muggle" can do. Most magicals have homes that a non-magical will be comfortable in and most magicals (especially those that live in the cities) are comfortable in the non-magical world. There are enclaves that reject all forms of technology (think Amish with spells) or prefer magic to technology but they aren't the majority and these communities aren't very large.
Marrying non-magicals have seen the word "Muggle" die out. It's hard to use that word (which sounds patronizing and slightly insulting) when your own mother or husband might be one. So the term "magical" and "non-magical" are used instead ("mundane" was in vogue for awhile but it has fallen out of use). Whenever Blaine hears Harry use "Muggle", he doesn't find it insulting, but he does find it amusing. It's like talking to your friend and he refers to cars as "horseless carriages" or computers as "counting machines" or people referring to asians as "orientals". It's an old word fallen out of use (and yes, still slightly insulting but Blaine is aware that he's in England now, he doesn't have to use the word but he's too well-mannered to impose his value system on others).
Important Places
Arkham – the largest settlement with a purely magical population (no non-magicals). It's larger than Hogsmeade and resembles a university town. This is where Miskatonic University is located. Because of the number of students from different enclaves (and different countries), Arkham is one of the safest places in the magical US. No one wants to start anything, especially with their children going to school there. It is possibly the most important territory of the Republic and has pretty much influenced their policy of being open-minded (to be prejudiced would mean less students, less students would bring in less revenue).
Salem – contains the second largest population of magicals in the US but they are hidden in pockets within the city of Salem (like Diagon Alley in London). This is the capital of Roanoke and Croatan and home to the Salem Witches' Institute (co-educational since 1905, every ten years or so there is a petition to change the name to either the Salem Institute of Magic or just the Salem Institute but so far it hasn't passed although most people call it the Salem Institute of Magic, the name hasn't officially changed yet).
New York City – a free city. No one enclave can lay claim to this city, instead there are areas within that belong to different enclaves. Greenwich Village, for example, is part of Roanoke and Croatan. This city has the largest population of magicals in the US, possibly in the entire North America. It is, however, a lawless city. The only law that is followed is the Statute of Secrecy. For the most part it is civilized but if you go out into territory not ruled by your enclave, you are on your own.
Miskatonic University – (see Magical Education) one of the largest schools of magic in the world. They teach the Hermetic Tradition (see Magical Traditions) but also have faculty members that teach other traditions as electives. They have students from different enclaves so Arkham is considered neutral territory although it is policed by constables from Roanoke and Croatan.
There are huge parts of North America (not just the US) that are unclaimed by the enclaves. Either because they hold no interest to the magicals or because they lack the manpower to oversee it. These are called "the Badlands" not because they are evil or corrupted but because there is no help to be found here. You are on your own. There are magical beasts that roam free and other magical beings that have piggy-backed with the other immigrants and moved out into the wilderness and are unregulated and unchecked.
If wizarding Europe is stuck in Victorian England, then the magical US is similar to the Wild West.