Well, I used to live in a small town in Taiwan. There is a high value placed on education in that culture. Children know that the best thing they can do to please their parents is to study hard, do well on exams, and that way become a professor or government official. Kids do not even get chores, because studying is the number one way to be a good kid.
I visited the Confucius temple in Beijing once, and it was inspiring to see the stone stelae in the courtyard engraved with the names of those who had passed the competitive exams to become magistrates throughout the dynasties.
I do miss students bringing me flowers on Confucius's birthday. I do not really miss parents telling me I could beat their children if they are bad. I asked a junior high student how his day at school had been once, and he said, "Pretty good, nobody hit me."
But the academic culture in Taiwan does not really encourage creative thinking or dissent. Students are discouraged from asking many questions or making comments. Rote memorization and imitating the model of the teacher is big. Cheating is tolerated, to a surprising extent.
So, no. I would not nominate Taiwan as the best environment for gifted kids.
I have been involved in educational research for some years now and am familiar with at least twenty educational systems. And although the educational systems vary a lot, I feel comfortable saying that socioeconomic status of parents as well as their education level (especially mother�s) have substantial influence on educational opportunities and outcomes of their children. I believe this to be true for gifted students as well. Of course it may seem that countries where gifted education is supported by the system, gifted children would have better opportunities, however, in most cases the access to gifted programs and/or better schools is provided based on achievement test scores. In Asian countries this means that parents spend a lot of money on tutors, and children are spending enormous amount of time preparing for these tests.
To answer your question, I would say Finland has the best home and school environment for gifted. Majority of parents are well educated, plus income inequality there is lower than in many other countries. Although its school system does not have gifted programs in place, it does have overall high education standards. Gifted children from different backgrounds(including ethnic minorities and immigrants) have more equal opportunities in the school system. In addition, their schools and teachers have freedom to adjust their curriculum to meet individual student needs. Actually it is an expectation not just a freedom to do so.
Recently I came across this BBC item about Finnish education. It is not specifically about gifted education, but the Education Minister mentions a pilot programme for gifted students. It's pretty exciting that they acknowledge the need for one.
Unfortunately, New Zealand is not the best country for the gifted. There are some excellent initiatives and individual schools that do well, but, in general, teachers are not well informed and academic achievement is not valued as much as it is in other countries that I'm familiar with. Sporting achievement is another matter. There is plenty of support for that.