If on top of having a job and getting GBI you still can't live in San Francisco, then you'd move to a cheaper area of the state/country.
What's interesting is that a lot of people flock to urban areas for the increased opportunity, but with a GBI, this may not be the case as much because there's less of a strain to make ends meet. This could reduce the cost of living in urban areas.
The federal basic income level would likely be based off of a national averages for cost of living, with state/city governments stepping in to provide greater subsidies if they feel it's needed. People may still need to pay more for convenience, but should have other options available, even if it means moving an hour or two away from the trendy metro areas.