Here, There and Everywhere
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A few years ago I made a trip through the deep South and had no trouble finding the types of towns you mention. Just a few that stick in my mind are Eatonton, GA home to the author of the Br'er Rabbit stories; Warm Springs, GA where FDR had his 'Little White House'; Selma, AL with history both old and new; and Natchez and Vicksburg, MS along the Mississippi where old plantations and Civil War sites intermingle. Actually finding charming towns in the south is not at all hard, you just have to look. There is usually a reality behind the stereotype.
AZBuck