The author never specifically says where or when this story is set.
However, it seems likely that it is set in the United States (the names, the general attitudes, the existence of the PTA all point to that). It also seems likely that it is set sometime in the 1950s (you have teachers hitting kids and washing their mouths out with soap and no one thinks it is strange).
Almost all of the story happens at the family dinner table. So I guess that is the physical setting for the majority of the story.
Overall, the setting is kept pretty vague. This is probably so that we get the feeling that it could be happening anywhere -- city, country, rich area, poor area, etc.
“Charles” has two main settings: the kitchen table, where Laurie talks to his parents, usually over lunch, about what has happened in school that day, and Laurie’s kindergarten classroom, in which all his stories take place. Not much information is given directly about these settings, nor are there any real details given about either; we learn everything through Laurie’s stories about Charles and the narrator’s stories about Laurie.
At home we have standard images of a family with a young son—parents asking their kindergartener how he likes school, Laurie eating bread and butter and cookies. The only incongruous thing about this setting is Laurie’s behavior. We have no indication that he was a disrespectful or ornery child before starting school, and yet he addresses his parents very casually, often insultingly. Our narrator, Laurie’s mother, assumes this is due to Charles’s influence in class. In this way, she interacts with the kindergarten only through her son’s stories, and Charles seems to be wreaking havoc in Laurie’s class—throwing chalk, hitting the teacher, making a little girl bleed… The tales of disruption and violence are endless. Laurie’s parents have no reason to suspect Laurie of any wrongdoing, and as long as the child keeps what happens in the story’s two settings separate, he is golden. However, a few weeks into his school career, his mother attends a PTA meeting, and with this action the home and the school settings intermingle. It is only here, when our two settings converge, that the truth about “Charles” is revealed.