I am NOT a native to Lafayette or LA in general. Just spent chunks of time there over the past 15yrs working in the offshore oil game. People out of LA i think often list New Orleans as THE place to eat in Louisiana. I get it BUT I highly prefer Lafayette as a city. When I pass through the state to Mississippi or Alabama, i prefer to drive around New Orleans and stop in Lafayette.
Some of my favorites are:
Zea's -
https://zearestaurants.com/location/lafayette/kinda pricey (but I usually expense this meal) but i think well worth it based on quality overall. There is a specific dish there called the twice fried duck. that thing is stupid good to me. Has a sticky, sweet sauce with a hint of fish suace and chillis. crispy, salty, slightly sweet, a little spicy and delicious.
The French Press -
https://thefrenchpresslafayette.com/This place is also pricey but generally not great. Zea's is overall better food for the price. BUT there is just a dish called the Cajun Eggs Benedict. I love dishes that are both familiar and yet new/novel. That's the way i felt about the Cajun Benedict. Btw, I still LOVE the classic Eggs Benedict.
Prejeans - as mentioned above
Laura's Two - A TRUE CAJUN GEMS!!!!!!!
Apparently they aint even got a website. Just a Facebook page. First of all, this is the type of place one think's of when you ask a local for their secret, non-tourist hot spot. Absolutely loved almost everything i tried. In true to south Louisiana style (which I adore), they have like cafeteria setup where they vary the meat sides a bit for a set box lunch. Usually involving a rice and bean of some sort.
I aint really eaten a turkey wing before and certainly aint never heard of a Stuffed Smoked Turjey wing before. My gosh that this is the proverbial slap-your-mama good.
Good luck. In case you can't tell, i like that city. good luck, hope u enjoy.