Speaking as a Mormon whose understanding of Mormon history comes from Pro-Mormon sources, here's my quick rundown:
The church started in New York. Problems arose because many aspects of the church clashed with popular religious sects, namely Joseph Smith's claims of angelic visitations and visions. His stories of using a "seer stone" to find and translate golden plates into the Book of Mormon was also very unusual and outside the boundaries of established Christianity. Those who did believe he'd uncovered some sort of treasure constantly harassed him and his family.
The church moved to Ohio. Things went well at first, but eventually Joseph Smith and several top church leaders tried to start a private bank. When the government refused to let them, they started a quasi-bank, trying to use legal loopholes, and even then they ran afoul of the law. The bank failed anyway, causing many to consider him a false prophet and causing a major schism in the church. Smith, and those loyal to him, were forced out of Ohio.
In Missouri, Mormon settlers experiences a culture clash with other Missourians. They were seen as prudish and judgmental. The Mormons believed the Missouri was "Zion," a utopia that Jesus himself would eventually reign over. Thus, they went around boasting that all of the land would soon be theirs, and that the wicked (non-Mormons) would be forced out. The Mormon society was very non-competitive: a Mormon would always trade with another Mormon over a non-Mormon, and they tended to vote en bloc for a single candidate, making them a dangerously powerful political factor. Eventually, the tensions came to a head and armed Mormons and anti-Mormon militias clashed, resulting in several casualties. The Missouri governor issued an extermination order to drive the Mormons out.
Next stop: Illinois. The Mormons began their own city, Nauvoo, which enabled them to craft a city charter that would prevent another Missouri situation from happening. However, many non-Mormons felt that the charter gave the church and its leaders too much power, resulting in an almost theocratic city leadership, with the power to raise a five thousand man army. Another schism in church leadership occurred, and the former Mormon leaders began to spread the word about Joseph Smith's polygamous marriages, embellished with rumors and speculation of a Mormon uprising. When Joseph Smith ordered their printing press destroyed, he was arrested and murdered in jail by an anti-Mormon militia.
Mormonism finally stuck in Utah. While there's still been plenty of clashes there, they've stayed put over the decades.
As you can see, Mormonism swept pretty consistently westward, never settling the south. Until the church really started sending out missionaries, it remained more or less centered in Utah, with remnants in the Northern states at it migrated.