As someone with kids that go to one of these independent prep schools (a rival of both SF University and Oakland College Prep), let me make a couple of observations. I know students and graduates from all of the San Francisco independent schools and .
First, as good as these schools are, they do not have the ability to just cajole their students into the most elite colleges. The high schools are difficult to get into, are very rigorous, and prepare the students well, but the kids still have to earn their admittance letters themselves. College counselling is mostly a matter of providing information and managing expectations, not magically opening doors to the Ivies. This is true for SF University and College Prep and all the others. Those days of “you go to the right prep school, you get into Yale automatically” have been gone for decades, and really only existed for a couple of boarding schools like Andover and Exeter anyway.
Second, the reason that a student chooses, say, Princeton over Stanford and Yale and where ever, is not because Princeton is more “hot.” It is almost always because the student got accepted by one and not by the others. Even at these schools, only the very top students in the class have a chance at that kind of opportunity, and even those students still get plenty of rejection letters from the most selective colleges. When the sample size is this small, there is too much noise for the data to mean anything.
Third, the big preferences are for urban over rural, Northern over Southern, “intellectual/artsy/nerdy” over “social/fratty”. Most kids who grow up in San Francisco want to be an urban environment. When I checked Naviance, I found that over a fifth of the class applied to NYU every year. Not because NYU was everyone’s first choice, but because so many of the kids could at least see the appeal of living in Manhattan. For a few of them, NYU was a top choice (especially if they were interested in acting), but for most it was a throw in or even a safety. Lots of applications to MIT, UChicago, Northwestern, WashU, USC, Tufts, Johns Hopkins, Tulane and Boston University and any other good college that is inside a city.
Many more applications to Yale, Columbia, Harvard and Penn and Brown than to Princeton, Dartmouth or Cornell, presumably for the same reason.
Meanwhile, there were less than ten applications, total, to Duke in a five year period. Less than ten to Rice or Vanderbilt or Emory or Virginia. Only 5 applications to Notre Dame and Wake Forest over 5 years. San Francisco kids have trouble envisioning themselves in the South or in the rural midwest, or at places that are perceived (correctly or not) to be either conservative or more social than intellectual.
If kids want to go rural, its almost always LACs. Each of the top LACs gets multiple applications every year.
Fourth, students are admitted to UC Berkeley but almost never attend. To get in, you need to be at the very top of the class grade-wise, and if you are at the very top of the class grade-wise at these schools, you are a tremendous student and probably also got into other elite schools. Berkeley also feels too close to home.
Anyhow, I don’t think you can get the information you are trying to scientifically create here. Your sample size is too small. But carry on.