"Sonny's Blues" is, like other works by James Baldwin, an examination of the dynamic between family members in the African American community. If one is looking for a central point the author is putting forward, it would be the hopelessness that pervades some members of the community juxtaposed with the ability of others to escape this feeling and to subsume it under other aspects of life, in which even the most oppressed people create their own values and survive.
Sonny's goal is to be a musician. Yet, understandably, his progress is impeded by the usual obstacles that confront anyone who tries to make a success of himself in the arts. There is also the specter of drugs which he must overcome. His brother, who narrates the story, is sympathetic but is not really a part of the milieu to which Sonny belongs and does not have the same visceral sensitivity to racial issues Sonny has. Or, he may be in denial about them. In asking Sonny what type of music he wishes to play, his brother mentions Louis Armstrong, but this reveals that he's almost in a separate universe of thought from Sonny, who doesn't respect Armstrong and associates Armstrong with a "down home" and outdated style. When Sonny mentions Bird (Charlie Parker) as his model, his brother seems unfamiliar with Parker but says, "I'll go out and buy the cat's records." This one exchange encapsulates the central theme of Baldwin's story in which there is a dichotomy of thought and of values between two brothers. The point is that different people react in individual ways to the dynamic of their own background. Sonny is a dreamer, a man on the outside who wants to fulfill those dreams but is beset by the external world and the way it impinges upon our desires—especially in the urban African American community of the time (the 1950s and 1960s) when the Civil Rights Movement was only in its infancy.
In formulating your thesis based on these factors, if you choose, you may wish to look at other books by James Baldwin such as his novel Go Tell it on the Mountain. In this story religion to some extent plays the role music has in "Sonny's Blues," as a counter-force to the unhappiness and oppressive environment in which young African Americans are growing up. Similarly, in a novel such as Richard Wright's The Outsider (unfortunately much less read than Wright's Native Son) the title character, Cross Damon, is a man who, like Sonny, has not "found himself" and is the Other, a man at odds with the normal expectations of establishing a secure working life for himself, raising a family, and so on. In "Sonny's Blues," Sonny's brother has achieved this "normal" goal, while Sonny remains an outsider attempting to follow his own path against the odds.