There are many examples of Atticus being fair and objective in the book, but here are just two that might help. I have included chapters rather than page numbers, simply because page numbers change with the different editions of the book.
In Ch. 2 Jem invites Walter Cunnigham over to lunch because he knows that his family is too poor to send one to school with him. It is then that we learn about the Cunninghams, how poor they really are, and how they pay Atticus for his services.
"I asked Atticus if Mr. Cunningham would ever pay us. 'Not in money' Atticus said, 'but before the year's out, I'll have been paid You watch.' We watched. One morning Jem and I found a load of stowed in the backyard. Later, a sack of hickory nuts appeared on the back steps. With Chrsitmas came a crate of smilax and holly. That spring when we found a crokersack full of turnip greens, Atticus said Mr. Cunningham had more than paid him" (Ch.2).
This shows how fair and objective Atticus is because he understands that the Cunnighams are poor because of circumstance. The depression has hit everyone hard, and farmers more than most. He is still willing to provide them with services and accept their alternative ways of paying him because he is a fair man. He does not see them as poor. He seems them as hard working people.
Later, in Ch. 11 when Scout asks what a "nigger" is, Atticus explains that the term is
"slipped into usage with some people like ourselves , when they want a common, ugly term to label somebody" (Ch.11).
He is very clear to Scout that he does not approve of the term and does not want her using it. Scout then asks Atticus if he is "a nigger-lover" and Atticus replies,
"I certainly am. I do my best to love everybody" (Ch.11)
Here we see Atticus doing his best to love everyone, in spite of some of the hateful things they might say. He is also trying to pass this same lesson on to Scout and Jem. He has taken Tom Robinson's case because he believes Tom deserves a fair trial, and despite people in the town and even in his own family (Francis) speaking ill of him for doing so, he is explaining that he tries to love everyone. That is about as fair and objective as they come!