<< I'm from Florida, but don't have any southern accent >>
Most harsh southern accents are from AL, MS, LA, TN, KY, SC, NC, WV, TX. Only Floridians in north FL and the panhandle (basically AL) seem to have southern accents.
BTW, I live in the south. I just think that harsh southern accents make people sound less intelligent. The best accent is no accent!!