A Montessori school, or at least a school with a strong Montessori background. It is where my child, at least, felt most at home (even though he's no longer there, our local school was just too small).
The Montessori schools allow kids to work at their own pace, and they can even set their own schedule to an extent. Depending on grade level, the teacher will assign a certain number of units of work in a particular subject each week. The children determine when they will do each subject, how quickly they will work, whether they will work deeper/further ahead/both, and learn a great deal of responsibility in the process. The learning is child directed and driven, but the parents might be able to have input depending on the school.
Because the children schedule themselves, they are able to focus on one subject for much longer than traditional schools usually allow, though I assume some kids choose not to. My son would do subjects in 2-3 hour blocks rather than the 30-40 minute class times he has in traditional school. It also seemed a much more languid and relaxed atmosphere, ironically enough, even though my son moved through more material there than he did in 3 years of traditional school.
When a child masters a level, s/he is allowed to move on, regardless of how the other students are performing. Most or all do not assign homework or grades, and mastery of content is more important than an arbitrary grade in a subject.
At my son's Montessori, there were also group lessons, though not every day. The groups were dependent not on age, but which children were ready for the material. That part was heaven for him as he enjoyed participating with the much older students, but perhaps not all Montessori schools provide group lessons.
There are some drawbacks, in that a kid who is obsessed with one subject can latch onto it even further to the detriment of other subjects (my son would sit and read the dictionary and study an atlas for hours...). Also, if the teacher doesn't have control of the class it can become noisy due to the way the schools are usually set up. But of the school types I've personally seen, I honestly believe it, in theory at least, comes closest to the ideal educational environment.
I don't have any person experience with it, but I also like the idea of a university style school with an emphasis on the classics. It seems to offer the best of both worlds- school with other children 2-3 days per week, homeschooling on the other days, and a pacing and depth that seems ideal for precocious children. I only wish that the ones in Texas were not so focused on the religious experience and more so on the academics, but somehow these classical schools have become synonymous with very conservative Baptist theology down here.
A gifted homeschool co-op would also seem great, but I'd worry about the same kinds of issues which have arisen in the GATE programs posters here lament, ie, that bright students are often admitted rather than truly gifted. Such a self-selecting group seems open to such issues. I can't speak to this issue since my son does not attend a school with a separate gifted program, and am only including that concern based on comments I've seen here.
Though if we asked my son what he wanted, the only available subjects would be math and tennis.
