Competition for the money is what keeps inflation down and also having it be a modest floor. For housing, health care, and higher education, the money floating around is specifically for those sectors. When coupled with limited availability / restricted competition, inflation easily occurs.

But if I can spend my money on a variety of things, then there is a lot more competition for me to figure out the value per dollar of a purchase.

In the specific instance of housing, the increased ability to move helps. What can also help is the ability for banks to be sure that people can pay. In areas with less pricey housing, a $100,000 house can lead to a 30-year mortgage at about $600 a month leaving $400 for other living expenses. This is a guarantee to the lender that the person can pay regardless of employment. And so suddenly a bunch of houses for poor people that are not economically viable because there is no lending for it suddenly become so. Not everyone will support it, but some will and that will ease up on pressures for apartments lowering that rent cost. It also could end the housing blight in many, many places without the truly inflationary process of gentrification.

The UBI is a floor and I would bet that prices would adjust to reflect that. If the floor is set too high, inflation will happen (imagine giving everyone a million dollars a month, it would certainly torpedo the current economy, but, assuming society somehow survived, new prices would probably change so that a minimal lifestyle require a million dollars a month). By setting the UBI at the current poverty threshold, it allows the poor to finally feel secure, it allows for the middle to save a little and feel less anxious/dependent on the good will of their boss, and for the rich, it keeps society stable enough that they won't have a revolution challenging them. All of this without doing too much damage.

Some things could end up with a higher price if the current wages are too low to worth being done by people who can now choose to walk away. This could be the case in industries where there is little profit being made and the workers are being paid very little. If there is a lot of profit, then I would presume the competition pressures would lead to the profits being diverted into wages rather than prices being inflated. Being money that can be used for anything would help keep some competition even in sectors that are monopolized.

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As an alternative approach, think of UBI as a dividend on our prosperity. Imagine that every American had enough ownership of stock to get a dividend pay out per year of $10,000. Would you ban the dividend pay out due to fears of inflation? The argument for the dividend approach is that prosperity comes from all of us contributing and so all of us should get a share of the profits of our society (private ownership is a creation of society and protected by society). And just like investors getting a dividend, the idea is that giving out that money is not only a useful reward for the lending of capital, but it also supports new investments and growth. The Citizen's Dividend does the same allowing each of us to invest in ourselves, and others, in ways to improve all of our lives.

A good narrative is that we are a species willing to be friends with one another and to be helpful to each other if we feel safe, secure, and supported. A CD (UBI) does just that.