Been discussed here a few times, but I'll chime in (again):
If you're a homegrown Texan (so consequently know what good Mexican and Tex-Mex is) DO NOT go to Superior. Locals think it's the best, but they think if you put sub-par fajitas on every dish, it constitutes as Mexican food.
Chimes would be the low/ entry level place to go for OK local/cajun food.
Parrains is a good step up from there, but could be a rough wait at certain times. Great gumbo and catfish atchafalaya.
For a unique spin on Cajun infused food that my wife and I really enjoy, try Building 5 in downtown. They rotate their menu, but the gumbo is always on it and is excellent.
While in town either pick up some world class boudin to take home from Jerry Lee's, or get it on your way home from Billy's in Scott, La (and don't forget to get a pepperjack boudin ball for the drive).
I shouldn't know this much about the area but my wife grew up in BR and family still lives there, so I'm there 3-4 times a year.