Fiji Airways has round-trip flights from Austin (AUS) to Nadi (NAN) for $746-$760 with a connection. Flights April, May, June, August, September, October, December, January, and February. Departures on Tuesday, Thursday, and Saturday. Extended weekends available. Origin/Destination reversible. No Christmas dates available.
Some small OTAs on Skyscanner have this for as low as $700; which is cheaper than the airline. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.
A Carry-on bag and also a personal item is allowed for free. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.