Most universities have a financial aid page where you can plug in your financial numbers and get an estimate of how much you would have to pay. They're called Net Price Calculators. Here is Cornell's webpage with a link to two different calculators:
https://finaid.cornell.edu/cos...cial-aid-calculators
I had one (non-baseball) child at an Ivy, and found that the amount they asked us to pay was, in fact, the amount we could afford to pay, without loans.
The wealthier the school, the more financial aid they offer.