Best barbeque towns in Lousiana? in Louisiana: Dining Posted July 6, 2010 In southwest Louisiana, look for barbecue at places where they say they serve Creole, which means something very different there than in New Orleans. There are some places in Lafayette, for instance. Laura's, where you might get Cajun rice dressing along with your barbecue chicken. Dwight's in Lafayette is very popular for barbecue but only on Sundays. There must be some barbecue in Baton Rouge, too, but I am not familiar with it. Louisiana may not be Texas nor Memphis when it comes to barbecue, but it's probably more unique for its sides, in my opinion.