| Cheap Flights: Austin to Havana $329-$333 r/t [August-November] â American Airlines / United American Airlines and United have round-trip flights from Austin (AUS) to Havana (HAV) for $329-$333 with a connection. Flights August to November. No Friday departures. Note that Cuba has additional requirements for entry. Review entry requirements at the US State Department website. Click for more details and booking links Cheap Flights: Austin to Havana $329-$333 r/t [August-November] â American Airlines / United . | 