I see a lot of people talking about intelligence and laziness. I have studied a number of inventors from the 19th and 20th centuries. My favorites are Philo T. Farnsworth and Nikola Tesla. Based on my own investigation of the topic, I found that self-motivation and self-control appear to be much more important factors in success and accomplishment than intelligence. The issue isn't that the educational system fails to accommodate prodigies, the issue is that the educational system isn't very good at teaching students how to motivate themselves. This applies to any student, not just those that are gifted.
In terms of raw academics, smaller schools provide a better quality education to the overall student body. In terms of social climate, smaller schools tend not to have as many of the large scale social problems experienced by larger institutions.
As a consequence of No-Child-Left-Behind, some school systems have really been struggling for financial support. Lately they have been using gender-segregation to improve test scores with dramatic results. There appear to be a lot of negative social mores influencing student achievement in mixed-gender situation (junior high/high school level). A lot of students intentional under-perform to avoid certain social stigmas, especially those related to the perception of the opposite gender.
I agree with a lot of the other posts that demonstrate concerns about the prodigy not being able to handle social and societal interaction beyond their prodigy. Based on my understanding of such matters, I would say that a small same-gender school would be the best way to proceed. It allows them to learn the rules and experiences of social interaction and society while limiting some of the academically detrimental factors.