This short story by Flannery O'Connor is narrated in the third person, so the narrator is what is referred to as "an omniscient narrator." Any of the thinking to which we are privy in this story, then, is through the viewpoint of the narrator. The deepest thinker, therefore, is the narrator in this story because we see everything through the narrator's vision.
However, if you must choose an actual character as the deepest thinker, you would have to go with the grandmother because her character is the focal point of the story. How she relates to the other members of the family in the car and how she relates to the Misfit when the family encounters him and his fellow criminals is what propels the drama of this story.
The author presents the grandmother as a very manipulative, quasi-religious woman, forcing her will upon her family. When the family encounters the Misfit, and they are all killed, the grandmother is left as the last one. She first tries to flatter the Misfit, then pleads with him, then tries to witness to him. This was her final mistake because the Misfit has issues with religion and shoots the grandmother, explaining that he is angry with God for not leaving any evidence of his existence. Before she is killed, the grandmother touches the Misfit, showing that she has afforded him grace and forgiveness. Her character has been transformed from the beginning of the story where she was concerned about people thinking she was a "good Christian" to actually becoming a good Christian, and offering grace, which is unmerited favor, and it is grace from God that saves all Christians, not works. The title, therefore, A Good Man is Hard to Find expresses a Biblical theme that:
"many are called, but few are chosen"
"it is easier for a rich man to go through the eye of a needle than to enter the kingdom of heaven."
Flannery O'Connor was a very religious Catholic and all of her stories have religious themes and motifs. You can read about her here on enotes.