<p>There are many colleges that aren't ivies with large endowments that can meet full need with mostly grants. Example - Duke, WashU, Emory, Northwestern, Chicago, then some LACs like Williams, Pomona, Swarthmore, etc. </p>
<p>These are only the ones I could think of off the top of my head, I'm sure there are several other schools that can meet most of your need with grants.</p>