“When in doubt, always choose Ivy (if somewhat affordable), then cost (UCB). Columbia opens the same doors as the others plus doors you don’t even know exist.”
This makes little sense and is bad advice. According to you, Columbia is preferred to UCB and Stanford or MIT if they offered more FA. Nobody, even Columbia students, would select Columbia over Stanford or MIT for engineering or CS even if all of the were the same cost. The Columbia SEAS students want to attend Stanford or MIT for grad school and rightly so since those are the gold standards. ucbalumnus brings up a good point about Wall Street, but CMU grads do really well there as again, their CS program is considered elite, Columbia’s is not.
Ynotgo brought up some real good points on Cal Tech, but here’s the thing - Cal Tech, CMU and Berkeley are very different wrt campus feel, school size and what they emphasize that a visit if to all three would probably decide it, if you haven’t already.