There are many people in your situation…those who can’t and/or would prefer not to pay their EFC. If that is the case, you will need to look for schools that offer merit scholarships and/or are have expensive COAs (cost of attendance).
Schools that offer need-based aid only sound like they won’t be options for you. I agree with econpop that you should not apply to schools that aren’t affordable, per their net price calculators. It’s ok to have some schools that on the list where attendance would hinge on getting one of their top scholarships, such as at Vanderbilt. Any of those schools/situations should be considered reaches.
What is your home state?