With that SAT, apply to Caltech. Your GPA is probably within range.
The advantage that you have for Caltech is in being female at that school, and majoring in CE. It is still largely a male campus. The UC’s don’t have that advantage anymore. (Other California privates like Harvey Mudd and Pomona are well known in California, but not so in other states)
Caltech is in Southern California, but is not as large as Berkeley (nor cold/rainy) and is a very small campus.
They do provide need-based funding (merit funding is very minimal since everyone has perfect scores/grades), which makes it affordable to most families.