Stanford is the top California Ivy. If a kid wants the prestige of the Ivy League in the California setting/weather, Stanford is that school.
Caltech is also outstanding but it is very STEM-focused – it’s not as well rounded, in terms of majors offered, as Stanford. I would call Caltech California Ivy #2 overall, with the caveat that in STEM they’re tippy-top.
The Claremont colleges are also outstanding, but they are LACs. You could refer to them as the California NESCACs I suppose. Oxy also – NESCAC-level.
The UC system is also outstanding, but they are public schools.
There are plenty of outstanding schools in CA, but in terms of an Ivy-like feel and prestige, I think it’s Stanford, followed by Caltech.
And a lot of kids these days want to go to school in California. That explains the number of applications (and resulting low admit rate).