It sounds like you are trying to generate support for an argument to your parents that they should either (a) spend double what they told you they could; or (b) borrow whatever they can’t pay for out of current income and savings. (You simply will not be able to get sufficient loans on your own to make up the gap, never mind the wisdom of it.)
Advocating for yourself is great. And you are doing the right thing by researching to see if there would be a return that would be worth the extra investment. But honestly, the answer is no, not even close.
No, internships and study abroad are not major or even significant factors in law school admission. See ^^. Top law school admissions is every bit as competitive as undergrad but nowhere near as holistic. There may be one short essay, but they are going to look far more at LSAT, GPA, courses taken, and maybe faculty recommendations. They also want to build diverse classes.
Assume 2 identical students, one from BU and one from UCD/UCSC/Poly. Identical majors, identical LSAT, GPA, etc. The BU kid is not going to have any “name recognition” plus over the others. There are a handful of schools that MIGHT make a difference like that, but BU isn’t one. So as far the top law schools are concerned, BU, UCD, UCSC and Cal Poly are all really good schools. They themselves might have “name” advantages over schools in lower tiers but hardly any amongst each other.
Frankly, east coast law schools would probably consider it a slight geographic plus to come from UCD, UCSC, or Poly.
I also don’t see why a kid from UCD/UCSC/Cal Poly could not study abroad or get internships, if that’s your thing.
So at the end of the day, if you take identical kids from BU and from one of your other choices, I would say their law school admissions chances are identical also. Therefore, the expected return on investment for the $160K extra spent on BU is literally zero.
And as a final matter, even if BU theoretically could provide a 5%, 10% or even 25% edge in law school admissions for an identical candidate, the payoff of going to a top law school STILL would have to be massive AND have a high probability in order for the ROI analysis to justify spending the extra on BU. But it’s not. Unless you graduate at the very top of a top law school, nobody has their pick of legal jobs anymore. The payoff of law school is determined far, far more by performance in law school and to an even greater extent one’s personal choices and abilities displayed in the working world.