Yes … but even if we had those statistics (easily searchable for many colleges over multiple years) they wouldn’t be too meaningful unless we could control for LSAT scores and GPAs. Those are the qualifications that seem to matter most in law school admission. I really doubt that T14 law schools strongly prefer applicants from one top ~50 college over another if the GPAs and scores are the same. Most likely, some colleges place more graduates at some T14 law schools either because more of their applicants are applying, or because they are applying with higher stats. If their average stats are higher, that probably is telegraphing greater undergraduate admission selectivity. I doubt Princeton, Harvard, Chicago or Michigan has any secret formula for raising their undergraduates’ LSAT scores (other that admitting more undergraduates with high SAT/ACT scores).
IMO, PhD production is potentially a more meaningful outcome metric.
First, the NSF publishes massive amounts of searchable data for many years, colleges, and disciplines.
Second, it’s fairly easy (though tedious) to normalize for undergraduate institution or program size.
Although it may be difficult to completely control for selection effects, I believe a PhD completion is more likely to reflect undergraduate treatment effects than a law or med school admission. Even admission to PhD programs hinges on more than GPAs and test scores. The maturity/focus of an applicant’s research interests also matters (sometimes quite a lot); this is more likely than LSAT/MCAT scores to be influenced by good undergraduate instruction and mentoring (particularly in the program we want to assess). To the extent PhD completion metrics (gathered for large populations over many years) reflect good undergraduate instruction and mentoring, they should matter even to people who have no interest in pursuing a doctorate.
Nevertheless there is much we don’t know (or possibly can’t know) from available information. So although statistics and rankings can be helpful in building an initial college application list, they aren’t necessarily a good basis for making a final choice (especially if used to justify a big price premium or a bad personal fit). The OP apparently already has his final choices. When all the choices are good, usually one of the first questions I like to ask is, “What’s the net price difference?” S/he hasn’t chimed in about that, nor about personal preferences (for weather, social life, sports, etc.)