Southwest has round-trip flights from Austin or San Antonio (AUS, SAT) to New Orleans (MSY) for $98-$118, NONSTOP or with a connection. $49-$59 each-way. Flights are in May and also August to October. Origin/Destination reversible.
Austin has Friday departures and Monday returns available for $59 each-way. Other days of the week vary in price, but the midweek is cheapest.
San Antonio has less weekend availability and the route has a stop.
Flight times vary depending on the date selected, most availability is either early in the morning or later in the evening.
Carry-on and checked bag are allowed for free. Southwest doesn’t charge change fees.