American Airlines has round-trip flights from Austin (AUS) to Grand Cayman, Costa Rica, Jamaica, or Nassau, Bahamas (GCM, LIR, MBJ, NAS) for $295-$350 with a connection. Flights August to November. Weekends available. Origin/Destination reversible. No Thanksgiving dates.
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.