| Nonstop Flights: Austin to/from Cancun $228 r/t [March-May + Weekends] â Southwest Southwest has round-trip flights from Austin (AUS) to Cancun (CUN) for $228, NONSTOP. $109-$119 each-way. March-May. Weekends available. Origin/Destination reversible. A negative COVID test result is required for re-entry. Southwest does not charge any change or cancellation fees. Click for more details and booking links Nonstop Flights: Austin to/from Cancun $228 r/t [March-May + Weekends] â Southwest . | 