OP, I’ll add that most of the houses that were posted and you will find, will require a car or personal vehicle of some kind. Being close to public mass transportation AND it being a standalone house, will probably bring you up to 6 figures for rent.
Make sure you do research on how to legally drive in Taiwan before deciding on the home!
Good luck! 
Just for the sake of it, I was looking into houses in Taipei on 591. Found one close to Longshan Temple and a couple in the Yangmingshan area. Not that expensive, less than 20k. as to teh state …
Oh and there was one so far into teh mountains of Xindian it was almost the Maokong gondola, but it was my favorite. nice little farm “with a plot for vegetables”.
Sounds lovely, but we have to be near the childrens’ school. So, we’re a little limited by that.
Are you choosing the children’s school first and then find a place to rent nearby, or doing the opposite?
We’re choosing the school first and then finding a place to rent nearby. Seems the most sensible way, given that our kids are still little.
You looking at downtown city public schools or also considering some of those “mountain” or “forest” public schools on outer edge of the city where the teaching and homework is less harsh?
Isn’t the school TAS or TES?
Not sure what you mean, but less homework sounds like something my kids would really love!!
Some stuff in those links with info on “forest schools”.
I remember there’s a Chinese link of all forest schools in Taipei and elsewhere, but cannot find it. Maybe someone else has it.
That’s something I’d like to check.
If anyone had this link, please share it!
I think some of them are listed here.
森林小學有特定指稱，
指的是人本基金會辦的小學
住校，一學期學費大約在十幾萬左右
台北市小學有所謂的開放學區，田園小學，
最有名的如陽明山上的平等國小，
作家凌拂曾為這間學校的老師
木柵區的指南國小，也是田園小學
公立的小學還有台北縣的直潭國小、雙峰國小、三峽的有木國小
往烏來的方向還可以看到廣興分校大大的雙子星學習計劃的廣告
台灣還有數間體制外小學，
因為森小為第一家，因此大多也被誤認為「森林小學」
但是其實這些學校的作法、理念差蠻多的
這類學校
如位於宜蘭的「慈心小學」是華德福的教育系統，
以史代納的「人智學」做為教育理論的根本
宜蘭還有「人文小學」是公辦民營的學校
台北縣除了森小外，
在烏來山區有種籽小學
新竹縣則有「雅歌」但是現在稱「大坪國小實驗計畫」
這些學校因為政府補助少，又堅持小班小校，
所以成本高，學費貴，會讓人以為學費昂貴在山上的小學。