I think it's pretty well established where the money is going, the answer being "to all kinds of stuff"
Physical plant and infrastructure. Sporting facilities, newer fancier dorms, more amenities for students, and so on.
There is usually some expensive academic initiative in play, the school playing out its ambition to become a Premier Something Or Other to attract more grant money.
There are more administrators and support staff across the board, with salaries and other expenses (chairs, offices, phones, computers, and so on).
What we do not have a firm answer to is "why?"
You can point to the professional administrator class and argue that bureaucrats, unchecked, will always find ways to expand the departments and thus their budgets endlessly. This is probably not wrong.
You can point to the fact that a university education is routinely valued at some high number in terms of lifetime earnings. A number I have seen is a $2M bump in lifetime earnings, then one can argue that in an unfettered market the correct price for tuition is: $2M, perhaps corrected for the time-value of money.
You can point to the availability of student loans being a factor that permits prices to drift upwards.
All of these things, and more, are probably true to one degree or another. None of them is a simple, pat, "why" and none of them suggest a simple solution. Markets are complicated.