There are plenty of cities with plenty of housing going vacant. In Baltimore, for example, it is a city designed for a million people with about 600k in residence. Houses go vacant, neighborhoods loose value, and the city dies. Why?
A large part of it is the lack of financial resources that the residents have. The lack of financial resources is directly related to redlining and the fact that Baltimore is a majority black city. But whatever the reason, money is what is required.
At $1000 a month, someone could take that UBI and spend half of it on a loan of $100k (30 years). That's a lot of capital and it could provide an individual with a home in Baltimore. A family would have even more capital to work with. This gives a great deal of flexibility and a lot of resources in neighborhoods without any. Further development would take place, giving these neighborhoods the kinds of businesses that wealthy white neighborhoods take for granted (such as grocery stores and banks).
What the UBI does is not just provide some financial amount right now, but a guarantee of future payments regardless. The risk of default would be far, far less and the promise of sustained financial reward for investment in these areas, without booting out the current residents, would be far greater.
If one also couples the UBI payments with a more aggressive tax on the wealthy, particularly on the ownership of multiple residential properties, then one could really damp down prices. From what I have read, several cities with massive housing price increases such as Vancouver and NYC have vast amounts of essentially vacant places because wealth has flowed into these places as wealth investment instead of living investment. But that policy is a separate one to consider, to be sure.
This country has plenty of resources. If we give people a minimum amount of money, those resources can start to be divided up much more equitably (peacefully, profitably) without the overt (and corrupting) hand of government deciding who gets exactly what.