The problem for you is that higher education in CA is dominated by the UC and CSU systems, and they are not particularly friendly to out-of-state transfer students, especially at the more popular and desirable campuses. Your best shots would be at the less popular UC or CSU campuses (which are often located in more remote or less appealing areas).
Private universities don’t discriminate against out-of-staters, but there are fewer of them than there are in the Northeast. The best-known privates (Stanford, USC, Caltech) are very selective. You would have a better shot at the less selective private schools; many of these are Catholic (U San Francisco, Santa Clara U, Loyola Marymount, U San Diego), but there are also secular options (U Pacific, U Redlands).
These less selective privates aren’t well known nationally, but can still be good. The University of San Diego, for example (not to be confused with UC San Diego or San Diego State U) currently has the same USNews “National University” ranking as Indiana. Santa Clara U is even more selective, but USNews currently ranks it separately in the “Regional University” category (because it doesn’t issue many research doctorates).