I believe free market will work. I feel most around here keep imagining how UBI will affect the CURRENT housing market which is mostly tied to the proximity to jobs. In fact UBI will significantly change this market. UBI will, in theory, get people stuck near "job hubs" with extremely high cost of living (most of that being rent) to move to more rural areas. They will no longer be tied to commuting 1h each way to work 40-60h a week to work a dead end soul sucking job just to spend 50% of income on rent and finally just move somewhere more hospitable and conducive to bettering themselves.

And also, you CAN build new houses in lots of places that are not the current "city centers".