I think you are overestimating the ease of people moving from one place to another. While job may be a primary reason people live in the cities, there are other important reasons like access to entertainment, shops, being close to other friends who leave nearby etc. It's not as simple as saying "oh, I could spare 500$ a month by moving in the middle of nowhere, let's do it". Not everybody wants to live in suburban/rural areas and spend most of his time at home.
> oh, I could spare 500$ a month by moving in the middle of nowhere, let's do it
For $500/mo sure. But if it's like people say and landlords try to raise rent $2k/mo like people are saying, then yes people would definitely move.
Also you could easily save $500/mo right now by moving from a big city to somewhere small. Right now, without UBI being a thing. The rent difference under a hypothetical UBI rent increase would be far more than $500/mo.
You think suburban people stay home all the time? What sort of overgeneralization is that? Suburbs = guaranteed vehicle = travel not just mandatory for commuting, but at will, as desired.