We are told in the beginning of the story that Jing Mei's mother is a Chinese immigrant who came to San Francisco in 1949. The reader can assume that the story takes place here, and Amy Tan throws in descriptions of different locales - The Mission District, an ethnically diverse neighborhood in San Francisco, and the fact that Jing - Mei live on Sacramento Street in Chinatown - to clarify this. Using references like the Ed Sullivan Show, the reader could also assume that it is most likely the mid 1960s.
Amy Tan's short story "Two Kinds" takes place in Chinatown in San Francisco in the years shortly after 1949. The time is likely the 1950s, as the main character and her mother watch Shirley Temple movies (already a bit old at this point) and the Ed Sullivan Show on television. This era was the second wave of Chinese immigration; the first wave, which started in the 1850s, was ended by various exclusion acts starting in the 1880s and continuing into the 1920s. After World War II, many Chinese people again began to immigrate to San Francisco, Los Angeles, and other parts of California and the west coast (and other parts of the country). The mother in the story has immigrated to California after losing a great deal in China, including her parents, her husband, and her older children. She wants to start a new life in California, and television, including the Ed Sullivan Show, and magazines are in part her guide to the way Americans should live.
Amy Tan's story "Two Kinds" is set in mid-century San Francisco. The family lives in Chinatown and the story relates the fact that they moved there in 1949.
The story moves from place to place in San Francisco, with some action taking place in the family's home and other action occurring at the piano instructor's home and at a talent show/recital.
The cultural setting is perhaps as important to the story as the physical setting. The narrator's mother is enamored with the idea that her daughter (the narrator) is a child prodigy who will bring pride to the family. Some of the mother's ideas are drawn from television (the Ed Sullivan show and other talent showcases) and from books like Ripley's Believe It or Not.
"The mother also reads countless 'stories about remarkable children' in the magazines she brings home from the houses she cleans" (eNotes).
These cultural influences help to shape the course of the story and serve as significant elements of the background. If not for the cultural thread promoting the notion of child prodigies, the narrator's mother may not have pushed her daughter to develop a talent.
This insistence from the mother is the animating tension of the story.