There is a very specific reason housing, healthcare and education costs are so high -- the government keeps subsidizing them in particular. Mortgage interest tax deduction, exclusion from capital gains tax, employer health insurance deduction, ACA subsidies, federal student loan interest deduction and subsidies, etc.
The problem with all of this is that it doesn't cause general inflation, it only raises the cost of those specific things. Which means in particular that it doesn't raise general wages, so the cost of those things increase relative to wages. On top of that most of those subsidies are to loan interest rather than principal, so the incentive is to take out a huge loan, which multiplies the effect on overall price. They really are very poorly designed policies. Unless you're a bank or an insurance company or an existing landlord.
A UBI is the opposite of that. It doesn't require you to do anything in particular, so it doesn't raise the price of anything in particular relative to everything else.
It also helps you out of the megopolis treadmill. The job in Pittsburgh pays $50,000, but the job in SF pays $150,000, so you take that one. Then you learn it costs $100,000 more to live in SF at the same quality of life, so you're really only just breaking even.
Add $12,000 worth of UBI and it becomes more advantageous to live in the median city than the huge megopolis, because the extra $12,000 goes further there and unlike the salary it's the same amount in both places. So more people do, and prices fall everywhere, because that's also more efficient. You increase economies of scale by increasing population in the smaller cities while reducing resource contention in the huge cities where economies of scale are already maxed out.
And likewise if you replace student loans and healthcare subsidies with the UBI, the cost of education and healthcare comes down, because then people don't lose any part of the subsidy if they choose a less expensive school or a higher deductible insurance policy, they just get to use it for something else. Like for patronizing service workers, which increases their wages relative to housing/healthcare/education.