The first Best Picture of the Year Oscar winner that had footage shot in Texas was also the first Best Picture of the Year winner, WINGS. This silent WWI aerial epic has my highest recommendation.
Two other Best Picture of the Year winners were shot in Texas. Can you name them? I'll make it easy for you. It's not GIANT, THE ALAMO, THE LAST PICTURE SHOW, TENDER MERCIES or PLACES IN THE HEART. All of these films were nominated for Best Picture but none of them won the award.