Housing is supply and demand. More demand for housing without an increase in supply will increase cost. That said, a guaranteed income may allow many people to safely choose to move out of an area that was hard to accomplish previously. If you're living paycheck to paycheck, how do you move far enough away from a high-cost area to actually reduce your housing cost while still allowing you to reach your job, since you can't quit it and still afford to pay rent? All you can usually do is trade commute time for rent cost, and then you pay in time and vehicle wear and gas.

UBI would allow an unprecedented level of freedom for people to relocate with little risk, and that would itself have a massive influence on city make-up and the housing market. If a lot of the unskilled labor in the bay area actually chose to move somewhere else, wages for those people would either have to increase greatly to meet demand, or the area would finally have to allow much more cheap housing.

I imagine other shifts like that would play out large in small in almost all aspects of the economy. UBI entirely changes everything.