Unemployment Insurance Question

I'm in Michigan, and losing my job (with a buyout/severance pkg) on April 30th. I'm moving in with my sister in California, in early May, and will be looking for work there. I know I'm still eligible for unemployment benefits even with the severance. Where do I apply for unemployment benefits? Would I apply in Michigan since my current employer is in Michigan, or would I apply in California since I'll be living there?

You would be getting benefits from Michigan, since that's where all your wages in the base period were earned. Filing in California will only delay your benefits, because then it will be an interstate claim.

If I were you, I would file online, to Michigan, on May 1, then you can report your address change when it becomes effective.