In Harper Lee's To Kill a Mockingbird, we are never really told how Atticus views himself. We are really only told how others view Atticus. Based on others' views of Atticus and certain things he says, we can speculate on the ways in which Atticus feels it is important to be seen--how he wants others to see him. If we know the ways in which Atticus wants to be seen, we can speculate on the ways in which Atticus views himself, provided we can believe Atticus sees himself as being successful in achieving his goals.
One way in which other characters view Atticus is as a very brave man. Scout particularly reflects on Atticus's bravery when she observes him nobly socializing with Mrs. Dubose, the reputed meanest old lady in the neighborhood. Despite the fact that the ill Mrs. Dubose always has a harsh, critical word to say to everyone, Atticus respectfully removes his hat in her presence, pays her a compliment, chats with her about the latest "courthouse news," tells her he "hoped with all his heart she'd have a good day tomorrow," shows affection to his daughter whom Mrs. Dubose had recently slandered, and heads home. In observing his ability to converse with and show kindness to Mrs. Dubose, Scout reflects, "It was times like these when I thought my father, who hated guns and had never been to any wars, was the bravest man who ever lived" (Ch. 11).
We also know Atticus feels it is important to teach his children what true bravery is. Atticus uses Mrs. Dubose to teach his children about bravery since he saw her as the "bravest person [he] ever knew" due to her determination to relinquish her morphine addiction, despite the fact that she was dying and in significant pain. Atticus explains the lesson in bravery he wanted to teach his children in his following speech to Jem:
I wanted you to see something about her--I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand. It's when you know you're licked before you begin but you begin anyway and you see it through no matter what. (Ch. 11)
Atticus's reference to being "licked" before you start something but starting anyway refers to his own decision to defend Tom Robinson since he knows it is unlikely he will be able to win the case, despite lack of incriminating evidence, due to the jury's racial prejudices, but he is determined to defend Robinson nonetheless because he knows it is the right thing to do. Therefore, Atticus's speech to Jem also reflects Atticus's own bravery, showing us that, not only does Atticus want his children to see what true bravery is, he wants them to see him as acting bravely. We can, therefore, speculate that Atticus sees himself as brave based on what we know of how he wants to be seen.