I agree with pohnpei that this Ray Bradbury short story is one that should appeal to all ages. The themes of the story, concerning the nuclear destruction of life on Earth, is certainly pertinent to all humans--especially at the time it was written, 1950, just five years after the atomic bombs were dropped over Japan. I have taught this story in high school (a combined 9th-10th grade science fiction class), and I believe the text in which it was included was from that approximate age group. The title was borrowed from a 19th century poem by Sara Teasdale.
I would think that Ray Bradbury would have hoped that everyone would read and understand this story. I think that because his message is that we need to get control of the technology that is threatening to control (and destroy) us.
I would think that his best hope for a target audience would have been relatively young adults. It would be this group that would have been more idealistic and likely to heed his message.
I would think that the older generation would have been more interested in getting their lives together and getting ahead after having lived through WWII and the Depression.