One interesting theme common to the stories in your question is the role music plays in the narratives. Both stories announce the centrality of music in their plots at the get go. In fact, Joyce Carol Oates's story “Where Are You Going, Where Have You Been" (1966) is dedicated to the singer and songwriter Bob Dylan. In "Sonny’s Blues" (1957) by James Baldwin, the inclusion of “blues” in the title immediately evokes both Sonny’s troubles and the genre of blues music.

The young protagonists of both stories—Sonny, and in the case of Oates’ story, Connie—have a deep relationship with music. As a musician, Sonny creates music to transform his pain, while as a listener, Connie uses songs to elevate her reality. To this extent, both Sonny and Connie are immersed in their music. The teenage Sonny is described as playing the piano every day from after school to suppertime, and “all day Saturday and all day Sunday.”

Connie’s ventures around town with her friends are lifted from their humdrum rhythm by the music playing in the backdrop at restaurants, malls, and cinema theaters.

They sat at the counter and crossed their legs at the ankles, their thin shoulders rigid with excitement, and listened to the music that made everything so good: the music was always in the background, like music at a church service; it was something to depend upon.

Music also exerts an almost addictive pull on both Sonny and Connie. In Sonny’s case, this quality of music-as-addiction has deeper meaning, because Sonny is also—or has been, for a long time—addicted to drugs. His immersion in music mirrors and sometime positively replaces his drug addiction. He explains to his skeptical older brother that the experience of playing music is like a heroin high, making one feel “in control.” Connie’s addiction to music is presented in more languid and seductive terms. For instance, walking to the car with a boy named Eddie, Connie's face is described as “gleaming with a joy that had nothing to do with Eddie or even this place; it might have been the music.”

Further, the role music plays in both stories has transformative and mystical aspects. In “Sonny’s Blues,” Sonny and his brother watch a group of “old-fashioned” revivalists sing hymns, such as “If I Could Only Hear My Mother Pray Again,” on the sidewalk. The older brother, who sometimes tends to view music as an unnecessary indulgence, notes how the singing appears to “suck the poison” out of one of the system of one of the enraptured singing "sisters". Sonny says he can identify with the singers because music puts him in the same state of ecstasy. We see the themes of spiritual transformation, religion, and music converge in the image of the singing revivalists, foreshadowing the story’s end.

In the story’s climax, Sonny’s brother finally watches Sonny play jazz at a nightclub and is lifted out of his indifference. Not only does he note the way playing music transforms Sonny’s crew on stage, he himself feels a spiritual awakening. The brother can finally see how Sonny’s music and suffering feed each other and how music transmutes this suffering. It can also be deduced that he realizes that as black men, he and Sonny are part of a heritage that uses music as a tool of resistance and as a means to transform pain.

Connie too, like Sonny, is misunderstood by authority figures in her life, who mistake her lightness for superficiality. However, it is towards the story’s terrifying denouement that we begin to see that Connie is capable of great sacrifice and selflessness, almost like a martyr. This spiritual transformation, which is (possibly) achieved by a sacrifice of the physical self, is loaded with Christian imagery and is accompanied constantly by music. When Arnold Fried shows up at Connie’s house when she is alone, there is music playing in his car, having its familiar lulling and seductive effect on her. Arnold Friend’s words, as he is trying to coax Connie out of the house, are described as “spoken with a slight rhythmic lilt, and Connie somehow recognized them—the echo of a song from last year, about a girl rushing into her boy friend's arms and coming home again....”

As Arnold Friend begins threaten Connie's family in an attempt to get her to come with him, Connie howls in pain and rage, creating a horrific kind of music into the phone, but does not dial a number. This is not because Connie is weak, but because she has made a decision to sacrifice herself for her family. Rather than risk staying indoors while Arnold Friend goes after her father, mother, and sister, she decides to step out into the unknown. When she finally steps out of the house, Connie experiences Arnold’s encouraging voice as a hypnotic “incantation.” However, she seizes some agency by letting the incantation evoke her self-sacrifice, uniting the story’s themes of evil, spiritual crisis and transformation, and music.

The previous educator provides some great ideas. I would add these:

• Both Sonny and Connie make choices that have devastating consequences. Sonny follows a path of addictions that alienates him from his family. Connie is promiscuous, and she allows Arnold Friend closer proximity than he should ever have been granted.
• Both Sonny and Connie face criticism that propels them to make poor choices. Sonny's dream is to play music, but the narrator scoffs at the idea. Sonny realizes that he will likely follow a path of drug use if he stays in Harlem, and he wants to get out. Yet his older brother forces him to give up his dream to do something more typical—and Sonny finds his way to drugs, just as he'd predicted. Connie faces constant criticism from her mother, who wishes she were more like her "plain" sister Jane. This inadvertently encourages Connie to be increasingly devious in her outings with friends, and she catches the eye of Arnold Friend at the diner. Neither Connie nor Sonny are truly accepted by those who should love them most.
• Both Sonny and Connie perform sacrificial acts in order to offer a path of healing to their families. Sonny doesn't just play that night; he performs with every ounce of his being. He leaves it all on the stage and risks his brother's rejection if he fails to meet the narrator's expectations. After all, this is the dream that his driven a wedge between the two for many years. Sonny plays with all the pent-up passions and anger and disappointment that he has kept inside so long, and as he plays, his brother is transformed, realizing for the first time his brother's true talents. Connie offers her own life as a sacrifice for her family. Arnold first tells her, "But if you don't come out we're gonna wait till your people come home and then they're all going to get it." And when she turns to leave with him, he encourages her by saying, "You're better than them because not a one of them would have done this for you." Thus, both Sonny and Connie walk into the unknown in an effort to redeem the broken relationships in their lives.

On first glance, these two stories are not obviously similar, so I can understand your having difficulties in formulating an essay. However, if we look more closely, we can find several points of comparison.

1. The two stories share a broad time period. James Baldwin wrote "Sonny's Blues" in 1957, but it continued to be anthologized as a relevant and timely story throughout the sixties, an era of significant cultural change in the United States and worldwide—particularly for minority communities. Oates's story was written in 1966, and it is set in a similar era of swift change.

2. Both stories focus on the difficulties faced by people marginalized by society during this time. Baldwin's narrator is a young black man who has managed to make a career for himself despite all the odds stacked against him by society and the place where he grew up. Oates's narrator is a teenage girl who is now facing difficulties in a world in which sexual morals are changing but she still very much does not hold the balance of power.

3. Both stories draw a contrast between the "solid" older sibling, as Oates describes June, and the malleable younger one. In both stories, the two siblings grow up in identical circumstances, but where one is able to become a responsible adult, the other is lured into a dark situation. In Oates's story, the situation is really not of Connie's own making; she is a victim of the fact that she, a young girl, cannot offer physical resistance to an older man who wants to bend her to his will. In Baldwin's, there is arguably some element of blame in Sonny himself for his own situation, but he has clearly been influenced by outside pressure. In each story, then, we can see an example of one person who is corrupted by a challenging environment, and one person who has somehow managed to escape it. In Baldwin's story, the reliable sibling is the narrator, and we witness his point of view. In Oates's, the point of view is that of the corrupted younger sibling.

4. Both stories have an ambiguous ending. At the end of "Sonny's Blues," although there is a moment of uplifting hope in the blues club, it is not at all clear what will become of Sonny. The same is true at the end of Oates's story—we are not told what will be the ultimate outcome for Connie. Both stories leave us feeling the same uncertainty that the characters in the stories have felt, growing up in the environments they inhabit.