with a UBI, you don't need a minimum wage. Also low end jobs will pay on top of a UBI, so it will be quite attractive if you don't have a lot of skills for higher paying work. Also with a UBI you have to balance it with a tax system that taxes wealth. In new zealand one of the advocates of UBI came up with a calculator for it ( simplified, but gives the idea of some of the levers you need to do it ) http://www.bigkahuna.org.nz/calculator/finance-minister.aspx

If you live in an area where there is a housing shortage, then yes, the market will drive things higher, but then a UBI lets people be a bit more mobile so people may move out of high rent areas more easily, also potentially driving up wages because less people are around to do needed work, but then as everyone gets pushed up, the tax will start to pull things back down. The whole point is income redistribution , especially in a society thats starts getting more and more automated.