All this would do is raise prices in the marginally cheaper places to live, in order of desirability. Sure it might reduce some prices in the core "superstar" cities, but not by a whole lot - since by definition those receiving a net-benefit from UBI are going to make less than average. Especially for a HCoL city.

Sure a few folks will drop out of the highly competitive professional job market to go homestead somewhere. They will be a rounding error, since they have already expressed revealed preference that "bare minimum lifestyle" is not enough. Someone capable of holding down a $350k/yr white collar job is already qualified to go make $70k/yr remotely in some random city anywhere in the US they want to live but they choose not to.

As we've seen with COVID remote work, the desirable "cheap" places to live will very rapidly have price appreciation because they are starting from such a low floor to begin with.

A $300/mo increase in some 30,000 population city in the midwest is a lot more material to the market than a $300/mo decrease for a $3k/mo apartment in a top 10 city core.

It also ignores the folks who want to live in the superstar cities but cannot currently afford to. If UBI is high enough to really matter, there will simply be a reshuffling. I'd expect upper-end to perhaps go down (largely due to increased taxes and thus less disposable income for the high earning group), but the lower-end to be raised eating up basically all the UBI surplus.

Also this totally ignores the third and fourth (and more!) order effects. If people are less incentivized to work, and work carries a much higher tax load (as it must for UBI to be worth even considering) - pay for high-end jobs must increase since working is going to have less net-benefit for an individual who now has a choice to totally drop out of the workforce and have others pay for everything. Who knows? Maybe prices actually increase in those superstar cities as they become even more winner-take-all environments?