In "Where Are You Going & Where Have You Been" by Oates is the central conflict internal or external, and what would be considered the two opposing conflicts in the story?

This is an interesting question, and one could easily argue that there are really two central conflicts: the internal ones that rage within Connie herself, and the one between Connie and Arnold when he shows up at her house. These are the opposing conflicts in Oates's story.
Connie's internal conflicts are centered on her desire to be noticed and valued for her beauty, even when that means breaking rules, defying her parents, and exemplifying the opposite of her sister June who is "plain and steady." The narrator describes Connie as having a dual, conflicting nature: "Everything about her had two sides to it, one for home and one for anywhere that was not home."  While she is at first flattered by Arnold Friend's attention, his interest in her becomes a serious problem.
While Connie's internal conflict is not at all unusual or potentially catastrophic in a fifteen-year-old girl, the conflict in which she becomes enmeshed with Arnold Friend is quite dangerous.  He is a predatory adult male with naive, vain Connie in his sights.  She is no match for his determination to have her, and at the moment he strikes, no one is available to help her. Ultimately, she is unable to help herself.  Readers are left to assume that the conflict ends badly for Connie.