Having to borrow $200K is crazy high for an undergraduate education. Heck, I always thought it was too much for doctors to graduate medical school with $200k in loans.
If the disparity were substantially less, then it may be an issue of penny-wise and pound foolish. Decades ago, I did forgo an opportunity to attend a lesser reputed college (also out of state) on full-ride(tuition, room/board, books/fees, travel) plus. I don't regret choosing the elite but my total debt was only a small fraction of the $200k facing the OP's DD. Were my kids to face the same choices, I might well nudge them toward the full-ride.
I'm pretty sure my choice was $100k in debt for Ivy League vs. free, and that was decades ago, so it hasn't been pretty for a long time.
Just looked it up again from a 1990's article, to confirm:
"For many students, the amount of aid is a major factor in deciding to attend one of the eight Ivy League institutions, where tuition is the highest in the nation, averaging $25,000 this year."
http://www.nytimes.com/1993/09/22/e...idding-war-for-prospective-students.html