If Yale is roughly the same price, it is no contest. The fact that it is actually cheaper is gravy.
I fully admit that I am prejudiced, but honestly, the constant drumbeat on CC that prestige “doesn’t matter” is pure nonsense. And in some fields it matters a lot. If she wants to live and work in the Nashville region, Vandy will have a stronger network. If she wants to live and work elsewhere, particularly abroad, Yale trounces Vandy.
This is not to say that Vandy isn’t a fine school with high standards and so on. This is not to say that people in every region of the USA faint at the mention of Yale. But let’s be realistic.