| Nonstop Flights: Austin or San Antonio to New Orleans $134-$156 r/t [August-November] â Southwest Southwest has round-trip flights from Austin or San Antonio (AUS/SAT) to New Orleans (MSY) for $134-$156, NONSTOP or with connections. $67-$78 each-way. Flights August to November. Extended weekends available. No Fridays. Departing San Antonio is cheaper than Austin. Southwest doesnât charge change, seat, or bag fee. American Airlines will probably match. Click for more details and booking links Nonstop Flights: Austin or San Antonio to New Orleans $134-$156 r/t [August-November] â Southwest . | 