Try the Netherlands. You can do a spousal visa with an unmarried partner, and if you come in on a highly-skilled migrant visa, your partner can do any kind of work. If you can apply to and get a job with a software company who can relocate you, that would be optimal.
I would check out /r/iwantout for some more general advice. Japan-dev.com is a good Japan-specific site, too.
Otherwise, it would be helpful if you could be more specific about where you're coming from and where you want to go. "Free education for children" is available in pretty much every developed country in the world.
Depending on your job experience and skills, I recommend Switzerland, the Czech Republic, and Japan.
Assuming youre an american: This will be hard to most countries that are developed if you dont have at least degrees, and preferrably masters. Her 1 year manual QA is not going to be easy. And the fact youre not married will make this all harder.
Your best bet is probably Japan or somewhere else in Asia where you can get dev sponsorship and she can get an English teaching job.
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My experience is that moving countries is very hard and you sound like you only have nebulous reasons for doing so, and it will probably not end up being a wise decision. Especially if you live in a big country, and you are escaping your past, doesn't it make more sense to move cities, instead? That is also hard enough in itself.