American Airlines has round-trip flights from Austin (AUS) to Antigua (ANU) for $356-$390 with a connection. Flights January to March. No Saturday departures. Very few extended weekends available. Origin/Destination reversible. The departure leg of this trip is a red-eye, early morning flight.
A Carry-on bag and also a personal item is allowed for free on American. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.