Hopefully, your kid doesn’t want to go to a school in NYC or SF.
I can’t speak to SF, but regarding NYC…
If you look hard enough, you can find a 3-bedroom apartment near Columbia for $300k. Same dealio with parts of Bklyn that are commutable to NYU, or even a 2-bedroom in parts of the East Village.
Taxes and maintenance $500-700/mo combined, no utilities other than electricity which may be included as well. Generally with income restrictions, but those can be in the mid-100s, and if the kid is officially buying it (perhaps via private mortgage), it’s doable.
NYC isn’t nearly as unaffordable as its reputation goes.