| Nonstop Flights: Austin to/from New Orleans $138 [June-November] (Weekends) â Southwest Southwest has round-trip flights from Austin (AUS) to New Orleans (MSY) for $138 with a connection. $69 each-way. Flights June to November. Weekends available. Origin/Destination reversible. Samâs Club is selling $500 Southwest gift cards for $449 [linked]. You can save an additional $50 on Southwest flights if you travel often enough or with a big enough group to burn through the gift card credit. Carry-on and checked bag are allowed for free. Southwest doesnât charge change fees. Use the fare calendar [linked] to pull up the fares. Click for more details and booking links Nonstop Flights: Austin to/from New Orleans $138 [June-November] (Weekends) â Southwest . | 