Granted, I live in the South, but I have always learned of him as an elitist adulterer who got himself shot. I had no idea about Jefferson's private scandals, for example, but learned about Hamilton's plenty.
This is really a question about modern popular attitudes about a historical figure, not the historical figure himself. Also, you're making a generalization with no evidence--in your education, Hamilton has been "demonized," so your question assumes that this is typical.
Hamilton was a politician, one of the driving forces behind the adoption of the Constitution and Secretary of the Treasury (and "prime minister") under President Washington. The debates over fiscal and foreign policies during Washington's two terms generated the first party system, of Federalists and Democratic-Republicans. Politics in the 1790s was extremely polarized. Hamilton was demonized in his own lifetime, just as Jefferson was. Hamilton is rightly considered the leading ideologue of the Federalist Party. This means that, by extension, he was the founder of American conservatism. Because conservatism and liberalism continue to be meaningful labels in American political discourse, Hamilton can be perceived as either a hero or a villain depending on who you're talking to. In periods of American history when liberalism is ascendant, historians who depict Hamilton as an evil monarchist will make more money.
You suspect that regionalism might have something to do with it. This might be because Jefferson was an important early advocate of state rights, which of course was the key justification for Southern secession 50 years later. Hamilton's talk about implied powers and the sovereign power of the national government were not the sort of thing that state interpositionists wanted to hear. So there's probably something to this. There are both state rights and nationalist flavors of American conservatism, and Hamilton obviously will appeal only to the latter.
If you would like to meet a Southerner who's a big fan of Hamilton, read the biography by Forrest McDonald.