I think your premise is flawed. First, I will assume you mean, Sicilian-American Mafia, Cosa Nostra. There were mafia families active in South, but as the South did not have as many large cities as the north, it was not as profitable in all cases, which is why you may think they did not expand there.

In Dallas, the Civello family was active which controlled the better part of Texas. In New Orleans, you had the Matranga family which controlled most things in the region. In Florida, you had all of the five families represented as well as the Trafficante family in Tampa. So the Southern United States had it's share of mafia, however the region was relatively poor and didn't have major urban centers which made gambling/prostitutions/other rackets profitable.

The mafia members were known to vacation in Hot Springs, AR. Before Las Vegas was a thing, Hot Springs had existed for gambling since the 1800's. Prior to the 1960's it was considered neutral by the mafia and used by many mafia as a hideout as it was far enough off the beaten path, while allowing gambling, and turning a blind eye to prostitution. Over the years more and more of the mafia were using Hot Springs as a vacation spot and for gambling well into the present. Hot Springs is also known as the place where Charles "Lucky" Luciano was arrested in 1936 and earned him a 30-50 year sentence, effectively ending his career in the United States. As well, the Gangster Museum of America is located in the city.

Are you asking about specifically the Italian Mafia, or using "Mafia" more generally as a term for any major organized crime syndicate?

The Southern states didn't have Italian communities as large as that of New York or New Jersey. In fact Italians were often discriminated against by whites (white southerners were incredibly racist).