Although your New York numbers are highly optimistic, I take your larger point. The UBI would be a basic income for someone living in a small town, would keep a roof over their head and enough to eat. In big cities it would be a bonus or subsidy you could either save or use if maybe you were choosing between two high pressure/high paying jobs and one paid somewhat less and was somewhat closer to what you actually liked doing. The extra $1,000 might make a difference. It would also mean landlords could require $12k less per year in minimum income to qualify for apartments.

It would still mean only people with very high paying jobs could live in New York (or as you suggested people who are willing to live with roommates and (at least for now) in the outer boroughs before they become too gentrified.

At the same time, I'll point out that the average studio in Manhattan costs $3115 and is 1 room only. Sharing 1 room with 3 roommates would currently be illegal, though certainly there are landlords who will do this under the table. You would still be paying $778.75 per month on average and would probably need to fill the room with 2 bunkbeds for 4 people (also illegal.)

Bloomberg introduced the idea of micro-apartments between 250 and 350 square feet and got some special loophole to allow them to go forward (previous law forbade units under 400 square feet) and these buildings have now opened under DeBlasio. They are still renting for $2600.

If I had an extra $1,000 per month I'd very likely use it to max out my 401k or put it in some other investment. If I were a new college grad or someone in a lower income job I'd still need to live way out at the farthest end of Brooklyn, Queens or the Bronx and maybe split a 1 or 2 bedroom with others. How I lived would still be largely determined by my job.