Purdue is a state school of the state of Indiana. Almost all public schools in the US are state schools (the few exceptions are schools like the military service academies).
As far as admission goes, UCM is probably a low match (and it does have ABET-accredited ME). UCR is probably a match. So is probably UCSC (though no ME, but it does have a reputable physics department). A whole bunch of CSUs offer ME, so if you apply to several of them (not just CPSLO and SDSU), it is unlikely that you will be rejected from all of them.
You are likely to be back here in April asking whether you should attend your “safety” that is really too expensive because it would involve a huge amount of debt because your parents will contribute much less than you believed (and people will reply telling you that you will have to attend your default safety of starting at a community college – a decent option in California, but probably a let-down for someone who seems to be turning up his nose at perfectly good schools).