In a modern first world economy (i.e. the only economy where UBI starts making some sense, and we're probably talking decades in the future so even more automation/productivity than now), the basket of goods that would be considered "basic" constitute something like <10% of total consumption and production. There would be some inflation caused by extra buying power, but it's not expected to be prohibitive in all the commoditized products such as food; I mean, the amount of consumed food would not change meaningfully as we feed pretty much everybody anyway, the only question is how the compensation is arranged - it doesn't matter that much for the economy if the poor unemployed person gets fed by food stamps, conditional social security, universal basic income, government supplied food packages, charity cash donations or charity soup kitchens.

One aspect that would change is the rental market. We would expect the landlords to try and capture much of that money. However, the big impact of UBI on rent is that it decouples the residental areas from the industrial areas; if you don't need to live where the jobs are and can credibly leave for a place where rents are cheaper, then some people will do so and that puts a limit on the rents.

As you state, small poor communities would feel a significant impact; however, in their case the main effect would be that they would become subsidized by the other parts of the society - much of the UBI they get would be spent on goods coming in from outside; their local market won't impact the price of a bottle of Coca Cola or a bag of potatoes, it's coming "from outside" anyway.

The cost of local services, on the other hand, would become much more spread out - if currently the cost for many services clusters around a single point (often close to minimum wage) because everybody needs a job so they do that service even if they don't want to; and everybody needs to eat, so they have to charge a reasonable amount even if they would be doing it as a hobby; In an UBI world you'd expect the cost of services to spread out widely so that services that are pleasant and interesting (for the provider) are cheaper than now, and services that suck for the workers become more expensive, as the workers now have a choice.