I think your mom may be pushing Berkeley because it’s cheaper. Have you had a thorough discussion with your parents about the cost of college, and what they’re really willing to pay? Too often students get accepted into their dream university, only for the parents to say they won’t pay for it. Even if parents have loads of money and resources, it doesn’t mean they want to spend it on tuition and housing.
As for as prestige of a university opening doors for you, I’d say it’s more important what you do and accomplish at whatever university you attend that will open doors. You should plan to pursue CS internships, develop your computing skills outside of your classes, take on leadership roles and participate in (and hopefully win) competitions while you’re pursuing your CS degree. These are the things that will open doors for you, and they are all within your reach regardless of which university you attend.
The best university for you is the one that is the best fit for what you want (out of state ideally), and what your parents feel good paying for (affordable to them). If you’re really a competitive applicant for the prestigious universities you mentioned, then you are also probably a competitive applicant for scholarships at a less competitive university that is out of state. I suggest considering universities that might offer you scholarships, where you could be happy leaving California while also keeping your parents happy.
My daughter dreamed of leaving Atlanta and attending a university in a snowy place. While she was admitted to Georgia Tech for a CS major and even had a full tuition scholarship there, she cried at the thought of going there. Instead, she wound up at the University of Minnesota with a stack of scholarships (and had her choice of many other universities with scholarship offers). She wound up choosing a different major in the end, but did so much computing on the side that she was offered a fellowship to pursue a PhD in Computer Science at another Big Ten university, even though she’d never even taken a CS course at her university. Once again, she chose a different major for her PhD, but is doing computing all the time. I share that to let you know that it is what YOU do in college that will open doors for you.
Go ahead and apply to your dream university of Northwestern as well as the other places you named, and also look into some places that might offer you a big scholarship.