As an alternative, consider Santa Clara U. They are a Catholic (Jesuit) school, but about half the enrollment is non-Catholic, and they don’t require participation in religious services. SCU has a core curriculum which includes some religion/theology/ethics courses, but the options are very broad (not just Catholic). The location in Silicon Valley is attractive to many smart and ambitious students; test scores are higher than at Pepperdine.
Other private options in CA might include U San Francisco and Loyola Marymount U (also Jesuit), U San Diego (Catholic but not Jesuit), and U Pacific and U Redlands (secular). However, since you are a California resident, the most affordable option is likely to be a UC or CSU. The privates are competitive options for out-of-staters, because the UCs and CSUs charge high out-of-state tuition with no financial aid. But for CA residents (like you), the low in-state tuition at UCs/CSUs is tough to beat.