If you live in Illinois, you'd use the addresses here https://www.irs.gov/filing/illinois-where-to-file-addresses-for-taxpayers-and-tax-professionals, which will be a CA address if you ARE NOT ENCLOSING A PAYMENT with the Form 8379.
And make sure you select the address next to the type of 1040 that you filed. You can also look at the Form 8379 instructions here https://www.irs.gov/pub/irs-pdf/i8379.pdf and look under Where to File and it will lead you to the IRS's website where you'll select Illinois and end up at the link provided above.
