"Okay. Tablet tablet on the wall, uh, speak of other ports of call?"

"Nice," she snorts.

The tablet comes up with a list of other human planets that are not currently part of the Radch and accept immigrants from it. There are forty, but if you limit to ones where you can immigrate without paying astoundingly high fees there are six. 

"Why do most of them charge so much?"

"I don't know things about international policy," says the tablet. "I think the Radch is not necessarily highly regarded outside its borders."

"Is it likely to matter to any of them that we aren't from here per se?"

"I don't know. Maybe? The true story also sounds implausible enough they might not believe it. I believe you because there are very few people in the world who could have constructed a convincing language from which some modern Earth languages are descended."

"Demonstrating magic won't help?"

The tablet thinks for a while and then says unhappily, "I'm a translation tablet."

"Yeah, sorry." Sigh.

"You could ask the Lord of the Radch for more money if you want to go somewhere that has a difficult immigration process."

"It isn't clear that she'd have incentive to enable that."

"She didn't say you couldn't leave."

"Yeah, but I'm not sure why she'd be interested in paying for me to do it."

The tablet can't come up with an answer there.

Well, the six inexpensive ones are a place to start, what are those like?

These two are theocracies that accept all converts, and this one is a theocracy that doesn't make you convert because they think people are more likely to convert once they live there. This one doesn't have a central government so there's no one doing border control. This one contains a hundred and twenty-two countries that won't let her immigrate and two that will, an anarchist state with principled objections to limiting immigration and a big former superpower in a fertility free-fall that'll take anyone under fifty. This one had a nuclear war and really needs more people to support their aging, irradiated population. 

...okay, what are the anarchists and the fertility-problems countries like?

The anarchists have some really great principles, though they've pissed off most of their neighbors since they take all these immigrants and many of them then sneak across the borders to somewhere that has enough infrastructure to support its population. There are constantly mutters about going to war with them, which in a sense would be easy since they are conscientious objectors to having a military or a police force, but no one wants to deal with the humanitarian disaster that'd inevitably ensure.

The big former superpower in a fertility free-fall is highly reviewed by former Radchaai immigrants; the cost of living is lower and it's otherwise much like home. The biggest complaint is that it's too hot to go outside ten months of the year. It has a president-for-life who some people blame for the fertility crisis since he started a lot of wars that killed off half the population of the wartime generation, though others argue that this is unreasonable, because the people killed mostly couldn't get pregnant. They are offering lots of subsidies for children now and hoping to turn things around; analysts think that if they can avoid a civil war when the president dies then they'll probably pull out of it fine.

There has to be some way for a time traveling magical girl and her twin brother to make a buck. She starts looking at expensive places; Xander goes to bed early.

These options look a lot better! Stable states with breathable atmospheres and no impending conflict - ("until the Tyrant gets bored", some reviewers note). Many of them are democracies, at least nominally, and one is an elective monarchy where the monarch is elected from the provincial governors based on their track record at province-governing, which has led to some spectacularly thriving provinces (as well as some failed ones). 

The elective monarchy sounds neat but she's getting tired. She materializes pajamas and goes to bed. In the morning she conjures up breakfast in the kitchen and puts on her standard outfit from memory; Xander starts figuring out prettier glove designs while she picks up the research on the elective monarchy.

The current monarch is monarch because as provincial governor they overhauled the education system and dramatically improved student happiness and student outcomes; the previous one got there by growing provincial production an average of 8% a year. Not all provinces take immigrants but the majority do, subject to varying requirements; a large fee and language proficiency and demonstrated job prospects, or a much larger fee for which they'll waive the language proficiency and the job prospects. Some provinces do the same re-education thing as the Radch but some do corporal punishment, or house arrest, or executions.

Can she find a hat trick of "takes immigrants", "prefers house arrest", and "no other glaring provincial flaws"?

Yep! Unsurprisingly it's one of the ones with the highest fees but Jasadr looks like a well-ruled place with most jobs in technology or medicine, a relaxed criminal justice system that prefers house arrest, and nothing else terrible mentioned on the reviews ("until the Tyrant gets bored").