In Berkeley, there's Caffe Giovanni and Lococo's. In Oakland, there's another Lococo's, run by cousins, different menu. You might try Trattoria la Siciliana, food's probably better than at any of those other places.
The local old-school Italian-American tradition e.g. Capp's Corner in SF is a little different from what you get in New Jersey, since most of the Italians here came from Genoa. Joey and Eddie's in SF is a riff on an old-school East Coast Italian-American place.