Well, "liveable" is going to be somewhat-subjective.
https://en.wikipedia.org/wiki/Open_border
Examples of open borders
Svalbard
Uniquely, the Norwegian special territory of Svalbard is an entirely visa-free zone. No person requires a visa or residence permit and anyone may live and work in Svalbard indefinitely, regardless of citizenship. The Svalbard Treaty grants treaty nationals equal right of abode as Norwegian nationals. So far, non-treaty nationals have been admitted visa-free as well. "Regulations concerning rejection and expulsion from Svalbard" are in force on a non-discriminatory basis. Grounds for exclusion include lack of means of support, and violation of laws or regulations.[52][53][54] Same-day visa-free transit at Oslo Airport is possible when travelling on non-stop flights to Svalbard.
That's not citizenship, but it's living and working there without restriction, which is probably about as good as someone's going to get in the present day. But it's probably colder than most people would like.
https://en.wikipedia.org/wiki/Svalbard
Approximately 60% of the archipelago is covered with glaciers, and the islands feature many mountains and fjords. The archipelago has an Arctic climate, although with significantly higher temperatures than other areas at the same latitude. The flora has adapted to take advantage of the long period of midnight sun to compensate for the polar night. Many seabirds use Svalbard as a breeding ground, and it is home to polar bears, reindeer, the Arctic fox, and certain marine mammals. Seven national parks and 23 nature-reserves cover two-thirds of the archipelago, protecting the largely untouched fragile environment.
EDIT: And income looks pretty solid, even by Western standards:
In 2006, the average income for economically active people was 494,700 kroner, 23% higher than on the mainland.
Converting to 2006 USD and then rolling forward inflation to December 2023, that'd be ~$110,463.54/year.
But part of the reason that they're gonna be paying that is because the people living there are gonna have to be living in polar twilight for a hefty chunk of the year.