I think adjusting by municipality is a bad idea.

A flat basic income across the country promotes migration to lower COL areas. An adjusted basic income promotes migration to higher COL areas in order to get a bigger income. While different areas having different COLs is pretty unavoidable, I don't think making high-COL areas more attractive is a good idea.

I'm also not a huge fan of adjusting for couples vs. single people. I get why they do it, it's an easy way to save money. But the actual expenses of you living with a roommate (as you suggested) compared to you living with a roommate that you're also sleeping with, don't change very much. (I have similar complaints about household income being used for basically everything except taxes, but that's a little further off topic.)