One question might be "How does Tan depict the merging of American and Chinese culture in the novel"? This may be refined to focus on specific characters, or it could be written as a comparison/contrast paper. You could discuss assimilation or clashing of cultures, depending on the circumstances and the characters. A good essay question will always be open-ended, without one clear answer. In fact, one key to a strong thesis statement is that it should be arguable. In you can't argue an opposing, then you don't have a strong thesis, or the prompt is poorly written.
In this case, as with all of Tan's novels, the central conflicts lay with the meeting of Eastern and Western cultures, often separated by decades in addition to distance. Otherwise, you could ask about the portrayal of female characters in the novel. Are some characters stronger than others? How are they affected by their surroundings? Tan always has powerful female characters, often dealing with "typical" issues: marriage, motherhood, careers, while balancing their heritage with the contemporary American influence.