A place to live is one of those examples i think, just not in the regions which are in demand. With a declining population and a push to live in more urban environments, there is quite a lot of living space in regions where its not attractive to live. You can witness the trend in Germany where alot of villages are dying out, as there are no jobs in the region and they are to far off for people to drive every day to work.
I see, that the trend to increased rent prices balancing out UBI would apply to in demand regions, but not at all in areas that would otherwise go unused. Most countries do have an extreme oversupply of living space, even before a population decline.
Let's go further with this. It's reasonable to assume that a UBI's cost would have to be offset by increased taxes, this would have to be progressive or the UBI would be pointless. So there would be a cutoff somewhere on the income distribution where the UBI payment would be offset by increased taxes, let's say at $80,000 to have a number. Making less than that, UBI would increase one's total take-home. Making more than that, the tax to support UBI would lessen one's total take-home.
The places with highly desirable real estate and high prices (e.g. SF and Manhattan) are already unaffordable to people making less than $80,000. So UBI would not increase the ability for residents to pay rent in those areas. Rather, it might actually decrease their net income, so by GP's argument it might lower rents in those areas. But in small towns (like City You've Never Heard Of, WV) with a low median income, UBI would increase net income. So it might increase rents there except those small towns are already emptying out as people leave to seek high-paying jobs in big cities, as you said.
So I think UBI would lead to rental/COL costs homogenizing somewhat rather than simply going up. It seems like this could solve several problems at once.
I see, that the trend to increased rent prices balancing out UBI would apply to in demand regions, but not at all in areas that would otherwise go unused. Most countries do have an extreme oversupply of living space, even before a population decline.