As everyone else is saying, it depends who I'm talking to and where I am. If I'm out of state, I'll say California, the Bay Area. If in-state, I'll name the city, (non-descrept suburb Fremont) but if I'm in another part of Calif, I might have to specify the BAy Area.
More pertinently, when someone asks where I'm from, I say Brooklyn. If they're familiar with NYC, I'll add Bedford-Stuyvesant. Everyone knows where Brooklyn is, and everyone there knows Bed-Stuy.
I've always appreciated Spike Lee for putting Bed-Stuy on the map, for better or worse.