Run the NPC’s at the private schools you are interested in and try to determine a value threshold. When my son applied privates (e.g. Vanderbilt, Rice) were 2-3x more than our state flagship (Michigan) and was a poor value. If the NPC shows a cost that is reasonable for your family and would work with a small amount of debt, then apply there.
Personally, I was shocked how expensive privates after the FA figures were returned and it made the decision fairly easy.