* Rebel Without a Cause (1955): This film, while set in Los Angeles, features a rebellious teenage character, not an adult.
* East of Eden (1955): Based on the novel by John Steinbeck, this film is set in California's Salinas Valley, not Texas.
* Giant (1956): This film, based on the novel by Edna Ferber, is set in Texas, but James Dean sadly did not live to see it released. He died in a car accident before filming was completed.
There seems to be some confusion in the question.