You get $10k more for living in SF over Nashville. Seriously, $10k? SF has to be somewhere around 50% more expensive than Nashville.
Taxes and rent costs blow away these piddly adjustments. Moving into SF from elsewhere requires _massive_ income adjustments.
I'd say an apartment here would cost $2000/mo more than Nashville. Gas is say 50% more expensive; let's say that's another $4K/year. That adds up to an additional $28K/year after tax; or, roughly $40K/year before tax.