Thanks for the responses - very helpful! Anyone else?

Contact the departments directly to see how successful they have been in getting graduates to the end goal of what you want to do.

Taking your example, for public health - contact the UG department that most closely aligns with that and find out what are the graduate school and career outcomes of recent grads from the last 5-10 years. Is there a pattern of grad schools or employers that the deparment is sending kids off to. Does this pattern align with your goals?

Lets take another example of yours - US History. If you child is interested in that - is she interested in pursuing a PhD in history, or perhaps using that to get into a top MA IR program (SAIS, Gtown, KSG etc), or maybe wants to teach HS or go into government -

well in that case, I would contact the history department and ask to speak to professors or administrators who have data on what graduates are doing after they finish and see how successful the program is in helping students get to their goals more often than not - and if that aligns with your ultimate goal.

For grad schools, US News does ranks by major (and even sub-specialty). You could use that as a guide.

Looking for tips/resources on assessing specific departments - not just "Is it a good STEM school (or Humanities school, or Arts schools, etc.)", but "Does it have a good Public Health (or U.S. History, or Dance, etc.) program". Any tips? TIA!