Delta has round-trip flights from Austin (AUS) to New Orleans (MSY) for $117-$137, NONSTOP. Flights May to December. Departures on Tuesday, Wednesday, and Saturday. Extended weekends available. Origin/Destination reversible. Dates over Christmas are available.
A Carry-on bag and also a personal item is allowed for free on Delta. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.