American Airlines has round-trip flights from Dallas (DFW) to Tokyo (NRT) for $1113, NONSTOP. Flights in August. Departures on Monday, Tuesday, Wednesday, and Sunday. Origin/Destination reversible.

Today’s USD/JPY exchange rate is the best it’s been for American tourists visiting Japan since 1986. It’s currently 163 USD per JPY at time of writing.
Prices for flights have been in an uptrend since February of this year, so flights are more expensive than they usually are, but I think that your overall costs will be lower due to cheaper Japanese goods/services when you arrive.
Previous deal for Tokyo was about $890, but had a connection. I think this is a good price for nonstop, round-trip.
Tokyo in August will be hot, but there is nothing stopping you from heading to cooler northern prefectures like Hokkaido which has an average historical high of about 78f.

American allows one carry-on bag, one checked-bag, and one personal item for free. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.

Read More Nonstop Flights: Dallas to/from Tokyo $1113 round-trip [August] – American Airlines