Hi, bat signal received. I'm here, and boy do I have thoughts. I'll try to organize them into a semi-logical order, but be prepared for a bit of an essay. My thoughts are directly related to living in China. As an aside, the educational systems in Southeast Asia (e.g., Thailand, Cambodia, etc.) are worse than they are in China. Singapore and Malaysia may be exceptions, but Singapore for sure is a very HCOL locale.
Within China, we need to separate the education systems between first tier cities (e.g., Shanghai, Beijing), second tier cities (e.g., Kunming, Suzhou, Chongqing), and third tier cities, as well as the very LCOL rest of rural China.
In first tier cities, you can choose between top international schools, international divisions of local schools, or local schools. Top international schools will run you around USD$30K-$40K per year for tuition. International divisions of local schools are approximately USD$20-$30K per year. Local schools or experimental schools (more hard core local schools) are around USD$12K-$15K per year.
Please disabuse yourself of the idea that "Asian schools are better" and "you can afford private school". It really depends on how you define 'better' and what you mean by 'afford'.
Let's start with the local public schools in first-tier cities. Teacher-student ratio is around 1:40. Students are publicly ranked, so every student knows where they fall on the totem pole compared to their classmates. Teachers use public shaming and scolding (sometimes bordering on verbal abuse by Western standards) to motivate students to work harder. Rote memorization (rather than critical thinking and problem solving skills) is the primary method of instruction. Independent thinking is not encouraged, unless it is in line with the teacher's. God forbid that you have a child with special needs. Learning support or even understanding of attentional or learning difficulties are non-existent. Your child will be labeled as either stupid or lazy if they show academic difficulties and you as the parent will be blamed for raising a stupid/lazy kid. High school students have approximately 3 to 4 hours (or more) homework per day. Your child will need to be proficient in Chinese, as local public school = taught in Chinese. Now, if your child is exceptionally bright, exceptionally hardworking and self-motivated, well-organized, and energetic, he/she will likely thrive in this environment (granted, he/she will likely thrive in pretty much any environment).
International divisions of local schools are like local schools but harder and more demanding. They often follow an IB (International Baccalaureate) programme which will allow your child to study abroad (outside of China) following graduation. Classes are taught in English. Everything else is the same as listed above, since it is still a Chinese system. Kids here tend to be wealthy Chinese kids. I believe other posters have already mentioned the crazy amount of comparison and "Keeping up with the Jones/Wangs/Chens" that occur in these schools.
So let's explore staying within the international community then at the international schools. These hire Western-trained teachers for the most part (except for the mandatory Chinese classes). They tend to be well-funded and thus have large, beautiful campuses with a ton of technology and resources. However, on the international circuit, your child must apply and interview for a spot in the good schools. Academic demands tend to be higher than in the local Western public school. For example, straight A students in your typical public school in Normaltown, USA, will likely be getting As and Bs at an international school. The pace of instruction moves faster and again, the students who are most likely to succeed are the strong students. Critical thinking skills ARE encouraged, and many of these students go on to attend good universities. Now, because we are China, most teachers are on two or three year contracts. This means that it is basically a crapshoot each year as to whether you will get a good teacher. Teacher turnover is quite high. Again, if your child has special needs or require special education services, you're not going to find much here, not matter what the brochure says. If services are needed, you will be paying out of pocket or paying additional fees.
Speaking of additional fees, the expensive schools will have annual school trips for the students that run between $1000-$2000 that are not part of the tuition. Don't forget fees for uniforms, fundraising endeavours, and keeping up with the Jones. The amount of wealth is insane here, and your child will need the newest iPhone (or at least an iPhone 7) if he/she wants to have friends and not be bullied/mocked at school. There is an undercurrent of comparison and often overt excess in the expat community. Having an ayi/maid and driver is the norm, not the exception. If your family doesn't have those, your child will likely feel left out. Yeah, frugal living habits is probably not going to happen in the typical international school.
Now, having said all this, there ARE ways to attend posh international schools cheap. I can think of two off the top of my head.
1) Get your company to send you over on an expat package. Your salary will be higher (due to hardship allowance), the company often pays for housing, a driver, flights back to home country for the entire family, health insurance for the family, and covers tuition fees for your children. As long as you don't take an excessive amount of exotic vacations while here, you should be able to save a chunk while living comfortably.
2) Get a teaching job at an international school. Your children can attend for free (though recent policy changes suggest that only one child can attend for free for each teacher teaching at the school). The school will cover housing, flights for the teacher back to home country, health insurance for the teacher only, and tuition fees for one child. You can live comfortably and save a good chunk. If you hang around other international teachers' children, your kids are less likely to be exposed to the opulence. They will likely feel poor compared to their peers.
With regard to college in China, your kids will need to take the Gao Kao (college entrance exam) in Chinese where they will be compared to every other graduating student and then ranked, which determines the colleges to which they can apply. At the college level, education focuses on rote memorization. I know because I used to teach at a local university.
If you choose to move to a second or third tier city for a lower cost of living, things are basically the same as above, but a several notches worse.
Anyway, take some time to do some real research before making this decision. My experience is based on living in a first tier city currently, teaching in a second tier city in the past, volunteering annually in a third tier city (mountain village school), with a spouse who is an international school teacher.