Prices will go up! So you are right! The immediate effect would definitely be inflationary. Underneath that, though, UBI would be a slight equalizing force on actual purchasing power. Therefore, I guess even in that inflated economy, there would be a bit more demand for apartments. Longer-term, this would mean that more would be built, I'd think.

I suspect that UBI is a very good idea, but also that its fans tend to ignore the second order effects and its critics tend to ignore its third-order effects, which are where I think the real benefits are.