The first thing that comes to mind is that rents would quickly adjust to extract as much money as possible from someone on UBI. And any increase on UBI would just lead to an increase in rent prices. People working while on UBI would squeeze those not working, or not earning enough, out of the housing market. Meaning people will probably need to work to afford living. So back to square one.

Now you need to figure out rent-control.

But that could screw up the construction market, reducing the incentive to build, and thus the supply. And quite possibly the quality of said supply.

And that’s just housing.

In reality, it's more likely that UBI-happy people would move to cheap backcountry while working people would move to more productive areas. Resulting in ghettos with little interaction between both groups. I wouldn't be surprised if over time one group decided it's about time to stop paying to strangers far away. Democratical process would be awesome too. With both groups split along UBI size.