If you're looking to immerse yourself in Cajun culture, try the Blue Moon Guesthouse. It's attached to the Blue Moon Saloon, so you might not get to bed early, but you'll be right there for all that's going on.
Jude's right -- The Blue Moon is a great place -- but busy -- and bring earplugs. It's kinda like a dorm without the students. Shared kitchen and some rooms have shared baths. I've stayed there when it wasn't busy and had a blast.
If you want a more laid back flavor, check Rocky's place, Bayou Cabins, Cracklin and Boudin, in Breaux Bridge. Very unique place. See this link:
http://www.bayoucabins.com/
Yeah, it's not exactly Lafayette proper, but it's an easy drive to Lafayette, and moreover, a quick drive to the basin where Pat's Atchafalaya Club and Angelle's Whiskey River is.
Got to give a thumbs up to Bayou Cabins. Stayed there two years ago. Food's great, people are great, you can take a picture of yourself with the giant crawfish in the parking lot, stare at the Teche while sitting on the deck. They had what I can only call a squirrel ferris wheel - an ear of corn on a propeller type device and watched squirrel figure out how to get to the corn. Built one as soon as I got how, and my dog sits and snickers as pay back for all the walnut shells they've throw at her over the years.
Steve
Got to agree with Griff. Cajun Country Cottages in Breaux Bridge are great. Ask to stay in the loft of the main house. Very affordable, and plenty of room. Ms. Sandy Vidrine is the manager and she cooks a mean breakfast. Sit on the front porch rockin' chair and play your box in time with the wind blowing through the spanish moss in the live oak trees. Stay away from the freeway, man!
JB
I've actually stayed at Rocky's place, and enjoyed it very much. He had a piano accordion up on the wall for decoration, and I got it down and -surprise!- it was playable. I'll see if the wife checked it.
I totally agree with the other posts...but if you
are looking for something more 'mainstream' and close
to everything, try the Comfort Inn just off HY 90 by
the airport. Within minutes of Mulates, Breaux Bridge,
Blue Moon and if you fly in, its right there. Clean
and cheap with free breakfast