Alaska and Hawaiian Airlines have round-trip flights from Dallas (DFW) to Honolulu (HNL) for $358-$380 with a connection. Flights January, February, March, April, May, July, August, and September. Departures on Monday, Tuesday, Wednesday, Thursday, and Sunday. No Fridays or Saturdays. Very few extended weekends available.
Some small OTAs on Skyscanner have this for as low as $342; 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 on Alaska Airlines. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.