This is a great question. Atticus is the obvious choice, but there are others who show integrity.
If we define integrity as doing what is right in all circumstances, then a few others stand out.
First, we have Ms. Maudie. She is consistently nice in the book. She treats all people alike - whether they are children, adults, black, or white. For instance, she shows extraordinary kindness to Jem, Scout, and Dill. She also shows kindness to Alexandra. Most of all she is also kind to the black folks in Maycomb. She sides with Atticus in the defense of Tom Robinson. In a conversation with Jem, she tries to explain that there are other good people in Maycomb - people with integrity. She says:
“We’re the safest folks in the world,” said Miss Maudie. “We’re so rarely called on to be Christians, but when we are, we’ve got men like Atticus to go for us.”
Jem grinned ruefully. “Wish the rest of the county thought that.” “You’d be surprised how many of us do.”
“Who?” Jem’s voice rose. “Who in this town did one thing to help Tom Robinson, just who?”
“His colored friends for one thing, and people like us. People like Judge Taylor. People like Mr. Heck Tate. Stop eating and start thinking, Jem. Did it ever strike you that Judge Taylor naming Atticus to defend that boy was no accident? That Judge Taylor might have had his reasons for naming him?”
Another character with integrity would be Boo Radley. Granted, he is a mysterious figure in the beginning of the book, but he only shows kindness and he does so in secret. At the end of the book, he saves Jem and Scout.
If we want to add another character, we can say that Calpurnia is another person with integrity. She defends the children to her friend at her black church.