As far as foreigner-friendly countries go, Taiwan and Singapore are great choices for you and your family to experience.That's awesome! What other countries in Asia would you recommend?
I never lived in Singapore long-term so I can't say much about it, but Taiwan (moreso, Taipei) is great for westerners wanting to get that Asian experience, but not stray too far from a "westernised" urban environment.
In terms of language, you can also get around Taiwan with just English as many Gen X/Millenials can speak it. Signs are mostly in Mandarin, but you'll frequently find them in dual languages.
The further south you go, the more "traditional" Taiwan becomes. Less English (and Mandarin!) speakers, more Taiwanese dialect speakers. That said, the scenery also gets progressively beautiful the closer you get to the centre, and the eastern side of the island is breathtaking.
Actually now that I think about it, one of the many people I met in Taiwan was home-schooled as well - their father was American while their mother was Taiwanese.
EDIT: Also, if you want affordable healthcare, then oh-ho-ho... Taiwan is a utopia for that. Even moreso than my home country.
EDIT 2: Living costs in Taiwan are also a third of what you'd probably be paying in the US. You can get a decent meal for about $4-5, and of generous portion too.
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