What would be a good research topic to write about for this book?
You said that you were writing a research paper, but you did not say if your paper was researching literary or historical-cultural aspects of this work, or both. In colege courses, often the instructor guides the students to write one or the other. You might clarify with your instructor what s/he wants. I see that the other two posters have suggested topics more along the cultural/historical line of research. This would be good if your instructor wants you to focus on the broader implications of the work, or the impact of historical political or cultural forces on the author and the work.
I will suggest some literary topics, so you can approach your instrucor with several ideas from each approach to this assignment. Of course, with the novel's being about Chinese-born and Chinese-American women, even the literary topics will have some of that influence in them as well.
1--Individual Choices and Consequeces: the characters' struggle to assert their own identities in a culture where women are expected to be obedient and submissive
2--Structure of the story: What does the story-within-a-story ("cradling") structure reveal about the characters' relationships and the cultural structure of the community? What does the revolving first-person narration reveal about the characters? What about the chapters where one character speaks for another? Why did Tan choose these narrative methods?
Also see the links below for more ideas. Enotes has great resources for essays on most major works of literature. Free!
Along the lines of the previous response, I think that one particularly interesting aspect of research would be to discuss the impact Tan's work had on the genre of cultural studies. There is much which is groundbreaking in the work. To discuss the narratives of women from China and first generation Chinese- American women was unique at the time. I think it would be interesting to trace the impact of this work on those Asian- American narratives that followed. At the time of Tan's writing, this was a field which did not have much in way of representation. Since that time, while more representation could be present, there has been more voices from this particular point of view and researching how Tan's work played a role in that growth might prove to be fascinating.
Throughout Amy Tan's "The Joy Luck Club" the ideologies of Buddaism and Confusianism influence the thinking of the characters and the relationship of these characters to each other since the Chinese parents want the American children to think like Chinese. So, while the generational differences are similar to many children, as well as other children of immigrants, the ideological differences are the main factor that contributes to the conflicts between the Chinese parents and their children.
The many allusions to Buddaism and Confusianism in Tan's novel can provide you with the threads that will connect your research to the narrative background of "The Joy Luck Club."
One area of research would be that of the history of the Chinese in the United States. While the mother in the novel comes to the United States right after World War II, there is a long and interesting history of the Chinese here, much of it not very pleasant.
Another area of research, since it forms the backdrop of the story, is the Japanese invasion of China, which was quite dreadful.
Still another area of research might be to research Chinese culture in general, and how it has been maintained (or not) in today's United States.
I am sure there will be other ideas offered here, but one of these might appeal to you. Good luck!
You could also address the mother/daughter relationships that are in the novel. There are the present day relationships between the four daughters and their mothers, but we also have the flash-back aspect of the way all of what is going on in the present is shaped by what happened to their mothers when they were children. There is the contrast between what the mothers experienced in China, that is wildly different from the San Francisco of the daughters' youth. As the daughters find out, in varying ways, about what their mothers experienced as children, it changes the way the daughters understand not only their mothers, but themselves.
Another teacher has mentioned researching the mother-daughter dynamics.
You could expand this by comparing the dynamics of the mother-daughter relationship in China versus that found in the United States. Part of what makes this novel so interesting is the differences between how the mothers and daughter view almost everything.
Backing it up a level, you could research how children and the family culture are viewed in China versus how they are viewed in the U.S.