The Chronicle of Higher Education (
www.chronicle.com) is the weekly newspaper of the profession of academe in the US (some of their articles are free, but many are pay-walled, so if you have access to a subscription via a local library, you should use that method to get to the restricted content. However, most of their statistical content is open-access.) The Chronicle does a nice job of breaking down where the money tends to go, and relatively little goes to teaching faculty. Most of what is paid in salaries goes to administrators, and at the very wealthy private schools, it isn't unheard of for the Director of Development to make as much or more than the President of the University. At schools with major sports programs, the men's football and basketball athletic staffs usually make more than the entire rest of the teaching faculty put together. Which is to say, the people who bring money in (in the form of grants and donations) also tend to rake it in personally. Medical schools are very prestigious, but also very expensive to run, because hospitals generate major costs in salaries, facilities, and risk-management costs. Some STEM faculty who are very good at parlaying research into patents will also be generously compensated; that tends to be standard because the patents are signed over to the school, though they may or many not generate income for it.
I've been in the academy for a very long time, and my job involves one of the most expensive aspects of maintaining accreditation: the library journal collections. Most laymen and even most professors have no clue what we have to pay for those. (And the price keeps getting higher; it has increased over 2000% since I started in this field in the early '80's. The average chemistry journal now costs a university at least $4K/yr. A university with a medical school normally has to spend upward of $3M/yr for journal access. FWIW, scientific output has been doubling every three years for the past two decades, which means more journals to buy as new fields develop; and of course, the equipment those fields require. Take mass spectrometry: it's been around since the 1920's, but it's full potential didn't become apparent until the 1980's. Since then it has become ubiquitous technology in almost every STEM field, and every STEM student learns the basics now. Hugely expensive machinery, and the number of journals that focus exclusively on research in the field has exploded. In the early 80's there were two journals dedicated to it, at last count this year there were over 3000 titles. Even if we only buy the top 10 of them that is still a major investment that didn't exist when I was a student.)
Still, the cost for undergraduate tuition is climbing faster than costs to provide it are, and the debt situation is beyond ridiculous. The Pell Grant program has been gutted, and most students who would have qualified for Pells thirty years ago now have to get that money from loan sources. One rule that I would like to see put into place is that no Federally-backed loans or grants should be given for attendance at for-profit schools, and that no Federally-backed loans should be given to students enrolled at private schools unless the schools agree to match those loans with in-kind discounts to the student. (If you want to diversify the socio-economic status of your student body, those low-income students shouldn't be the ones paying interest for that goal.)