| Cheap Flights: Austin to/from Panama City, Panama $336-$339 r/t [May-March] â American Airlines / United American Airlines and United have round-trip flights from Austin (AUS) to Panama City, Panama (PTY) for $336-$339 with a connection. Flights May to March. Weekends available. Origin/Destination reversible. American fare is Main Cabin, not basic. A Carry-on bag, personal item, and seat selection is allowed for free on American. United fare is basic economy, fees for carry-on bags and seat selection. Click for more details and booking links Cheap Flights: Austin to/from Panama City, Panama $336-$339 r/t [May-March] â American Airlines / United . | 