Rent is already quite high in capital cities, generally based on what high income earners can afford. I think a basic income is more likely to match an average wage so shouldn't result in higher rent. If anything it should take some pressure off housing in the capital cities if one doesn't have to live there so they can gain some mediocre form of work. Though this might result in higher rent in regional areas, as people discover that the basic income would allow them to live comfortably there. The government in turn would have to ensure there is affordable quality housing available close to employment.