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United & Air New Zealand have some decent flights to Houston. Not the cheapest ever but decent as it includes summer. Looks like there are dates from July to November. Fares include bags, meals and seat selection.
Find the cheap dates via Google Flights then plug them into STA Travel or Skyscanner.
Went to Houston a couple of years ago and was an interesting place albeit you really need a car to get around. The Space Center and Rodeo Houston are well worth it not to mention the amazing smoked BBQ places. Can also recommend San Antonio and Austin.
