The starting point of defining irony might help here. The critical element in the definition is the idea of incongruity:
.... [a] situation in which there is a sharp incongruity or discordance that goes beyond the simple and evident intention of words or actions. Ironic statements (verbal irony) often convey a meaning exactly opposite from their literal meaning.
We can see this at several points in the story. Consider Arnold Friend's name written on his gold jalopy: "A. Friend." Arnold is about the most divergent example of a friend that one could envision. Another irony is Connie, herself. Connie is shown as the typical teen who loves and revels her independence, something of which she is in perceived considerable control. This is ironic between at the end of the story, she is nowhere near in control of her identity and the situation in which she is at the end of the story. I would also think that the title of the story is ironic. Connie's parents are so detached from her state of being in the world that they cannot even ask the fundamental questions of "Where are you going?" or "Where have you been?" The irony of this is not missed given the ending of the story. Oates might be suggesting that had the parents been able to ask such questions and ascertain such answers, Connie's interaction with "A. Friend" might not have needed to have happened.
Perhaps the best aspect of irony in Carol Joyce Oates's story is in its concept of contradiction between what seems to be and what actually is.
While there are several instances of irony in "Where Are You Going, Where Have You Been?" the strongest impact comes from the irony of the depiction of the main character, Connie, which is immediately suggested by the story title that conveys misdirection and delusion. Because Connie "knew she was pretty and that was everything" to her, she fills her mind with "trashy daydreams" and indulges her carnal desires to the point that she is deluded about reality and ignores any advice from her mother. While Connie believes that this rejection of the values of her mother and family allows her more time to engage in pleasure, she later learns that the results of her consuming eroticism are, ironically, just the opposite.
So, by the indulgence of her carnal pleasures, which the "shaggy black-haired" Arnold Friend notices--"He wagged a finger and laughed" as Connie accompanies a boy named Eddie to his car--Connie herself unwittingly invites the devilish Arnold Friend to come for her. Thus, a great irony occurs because while Connie has a delightful time indulging her sexual fantasies as she engages her mind in erotic daydreams, necking with boys in their cars, and listening to music that arouses lustful thoughts despite her mother's attempts to "drag her back to the daylight by finding things for her to do," she opens herself to the deadly dangers of this eroticism. What appears to be a youthful embrace of life and all its pleasures ultimately leads to their opposite: fear, suffering, and death.