“The World’s Most Famous Cajun Restaurant” is the claim. Mulate’s is near the Convention Center so you’ll encounter plenty of conventioneers, tourists and other folk who are trying to discern the difference between “Cajun,” “Creole,” creosote and/or the Cretaceous period of l35 million years ago. Cajun bands play nightly with food served from 11 a.m. until 11 p.m.