American Airlines has round-trip flights from Austin (AUS) to Grand Cayman (GCM) for $285-$293 with a connection. Flights January to May. Weekends available. Origin/Destination reversible.
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.
Hopper has a coupon for -$200 off Cayman Hotels.