Why don't you drive about 45 minutes away and go to Lafite's Landing in Donaldsonville. Chef John Flose's restaurant at the Bittersweet Plantation, also a Bed & Breakfast.
Though not inexpensive, the food and the ambiance of this small little town is memorable.
Just for your information, Lafitte's Landing was destroyed by fire some time ago and Folse has re-loacted to Bittersweet. I've not eaten there but heard mixed reviews Although several respected friends reported fine dinners at the old Lafitte's, I found it fine but not ecstacy-inducing.(I have an aversion to squiggle souces on plates. too much hooey.)
I'm including a link to the Austin Chronicle's Guide To Southwestern Louisiana, which I found to be very helpful in my moseying around Cajun country.
I especially recommend the Palace Diner in Opelousas, and the Tabasco factory at Avery Island.
One note: This guide is written from the perspective of Austinites making a road trip, so the itinerary will be sort of backwards from N.O.
The absolute best place to dine in New Orleans is Marisol. It's at the edge of the French Quarter, has a great patio and delicious, inventive food. Also, tour Blaine Kern's Mardi Gras World to see MG floats being built. On Xmas Eve drive from New Orleans to Grammercy along the river to see the bonfires.