The threat of violence is everywhere in the story, but we never explicitly see it. Words, more than actions, define the characters in the story. Most of the drama takes place in the dialogue between Connie and Arnold. It's through their verbal interactions with one another that we get a sense of Arnold's charisma and general bad-guy vibe, as well as Connie's transition from naïve teenager to (possibly) a more mature, moral agent.
The characters are living in an image-obsessed culture, with rock-and-roll stars and movie celebrities as iconic figures. (So, not much has changed since the 1960s.) Their sense of themselves and others is largely defined by the way they look. We're told repeatedly how "pretty" Connie is, and her interactions with others are largely determined by how they feel about her prettiness: men are attracted to it, her mother seems to be threatened by it, and her sister is indifferent. Arnold is able to use this image obsession to his advantage; despite his age, he can pass as a teenager by dressing like the kind of rebellious teen popularized in Rebel Without a Cause.
Oates was originally thinking of including this story in a collection of short stories about the different forms of love (source). In "Where Are You Going?" characters' attitudes toward sex and love constitute a large part of who they are. We get a full range of attitudes, from Connie's mother's disillusioned domesticity, to Connie's romantic fantasies, to Arnold's sexually explicit threats.