I live about 12 miles north of Avery Island. This is ground zero for Cajun food. New Orleans may get the edge for creole cooking, but if you really want authentic Cajun, Lafayette/New Iberia/Broussard/St. Martinville/Abbeville are where you want to go. I live pretty much in the middle of all those :)
On one trip to Louisiana we were driving in your direction and stopped at an abandoned plantation house. the sign said The Old Homeplace, I think. I can't remember the road but driving south the levee for the Mississippi was on your left and the house was on your right.
It was in terrible rundown condition but someone had put a red metal roof on it so I hope by this time it has been restored and is open to the public.