If "working with microprocessors" means designing them as in working at the Intel design sites at Santa Clara or Hillsboro then you probably want an EE degree. Which school is the "best" school near the west coast... will just cause an argument.
However, what you might want to look at is top rated schools. Which those are depends heavily on who is doing the ratings, but Cal Tech, UCLA, UCB and Stanford are usually up there. Other good schools are UCSD and UCSB. USC is rated highly in some rankings but it's not exactly near the coast (kind of a nasty neighborhood actually). The Cal State schools are usually not rated as highly as the schools above (although that depends on the degree and what you want to do with it). The cost of the private universities may (or may not) be a significant factor.
I suggest you talk to your high school guidance counselor to make sure you are taking the right classes to end up with the right classes in the end. I also suggest you try to talk to a recruiter at a couple schools you are interested in to find out what they are looking for. High school guidance counselors can sometimes be surprisingly ignorant about that type of thing. And lastly try to talk to people that went to your high school that got into the schools you are interested in and a couple people who working in the industry you are interested in. I suppose it depends on the high school but I think AP calculus, AP chemistry and AP physics are likely to be high priority goals both in terms of preparation as well as university acceptance for an engineering degree.
If you want to work supporting operations at Intel for example, a BS in CS and few years of experience was good a while back (if you wanted to get into their system administration department for instance). I know someone who got a Ph.d in EE at UCLA and got a great job at Intel actually working on microprocessor design. Of course, a Ph.d from a school like UCLA is a major undertaking and that's why I think it's important to find out if that is really what you want to do.