Delta has round-trip flights from Dallas (DFW) to Tokyo (HND) for $754 with a connection. Flights February, March, April, May, June, August, September, October, November, and December. Departures on Monday, Tuesday, Wednesday, and Sunday. Dates over Christmas are available.
A Carry-on bag and also a personal item is allowed for free on Delta. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.