American Airlines has round-trip flights from San Antonio or Austin (SAT, AUS) to Saint Croix (STX) for $213-$251 with a connection. San Antonio flights in April. Austin flights in April, May, December, January, and February.
Flights out of San Antonio are cheapest (about $213 on the low end), but the availability is pretty limited out of that airport.
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.