In "To Kill a Mockingbird," with whom do the children sit in the courtroom?

Significantly, the children sit in the balcony, reserved for the Negroe population of the town.  This action ties to the previous one of Calpurnia's having taken the children to her church one Sunday.  But, while some of the congregation resent Jem and Scout's attendance at their private church, they do not express any negative feelings towards the children who sit in their place in the Maycomb courtroom.

The significance of the children's being seated in this section is that they are separated from the prejudiced audience and are elevated and distanced from the people involved in the trial.  This perspective allows Scout to observe her father's actions and words with a maturing objectivity and analysis. (developing the theme of maturation in the novel as bildungsroman).  In Chapter 17, for instance, Scout observes, "Something had been made plain to Atticus also, and it brought him to his feet" when the Sherriff testifies.  Then, in Chapter 19 when Tom Robinson answers the questions of Atticus, Scout remarks,

Atticus sometimes said that one way to tell whether a witness was lying or telling the truth was to listen rather than watch:  I applied his test--Tom denied it three times in one breath, but quietly, with no hint of whining in his voice, and I found myself believing him in spite of his protesting too much.

Later, as Atticus leaves the courtroom, someone touches Scout, "Mis Jean Louise, stand up Your father's passin'."  Indeed, from their position in the balcony, Scout and Jem both learn much of those with whom they sit as well as of life.