If we describe justice as being fair, reasonable, and treating others with a moral and equitable rightfulness, then Atticus, more than any other character in To Kill a Mockingbird, consistently exhibits justice. In fact, many people would think Atticus treats others (such as Bob Ewell) too fairly.
In Chapter 23, Atticus says, "I wish Bob Ewell wouldn't chew tobacco." Ewell confronted Atticus at the post office, spit on him, and challenged him to fight. Atticus just took it and left. Jem, worried about his family's safety, asks Atticus if he's worried about Bob Ewell. Atticus says this is just Ewell's way of dealing with his problems. Atticus says:
So if spitting in my face and threatening me saved Mayella Ewell one extra beating, that’s something I’ll gladly take.
This is not a case where Atticus is concerned with Bob Ewell. He is thinking of Mayella. Mayella never had a real chance growing up in the Ewell house. Although temporary, and Mayella would never know about it, Atticus takes Bob's frustrations so Mayella won't have to. Atticus sees this as the just thing to do for Mayella.
Strangely enough, it may be difficult to find quotes about justice in a book where injustice predominates. Look for subtle examples such as this one.
The most obvious example, and one which Atticus is not totally comfortable with, is Bob Ewell's death. Bob Ewell's lies led to Tom's conviction which led to Tom's death. Bob Ewell attacked the children, making his words and deeds dangerous. Although Atticus wants Bob's death to go through the courts, Mr. Tate insists that Ewell fell on his knife. He says:
There’s a black boy dead for no reason, and the man responsible for it’s dead. Let the dead bury the dead this time, Mr. Finch. Let the dead bury the dead. (Chapter 30)
Because of Tate's persistence, justice was done for Bob Ewell. Just as importantly, justice was done by not subjecting Jem to a trial. And according to Tate, it would be wrong to subject Boo to such a thing as well:
To my way of thinkin’, Mr. Finch, taking the one man who’s done you and this town a great service an‘ draggin’ him with his shy ways into the limelight—to me, that’s a sin.
Scout agrees, telling Atticus that it would be like shooting a mockingbird. In this case with Jem and Boo, justice is not making sure a punishment fits a crime. Justice is making sure innocent people are treated with consideration and respect.