Maybe a point to be made. When people visit Lafayette they expect all the food to be "Cajun". In reality the food offerings are extremely varied. People in this area know good food no matter the culinary region it originates from and you won't last long serving bad food.
CajunAmos has a good list noted above. I will add that the FrenchPress mentioned by many is a restaurant that was nominated for a James Beard award last year.