Less than $30K and prestige will be very tough. National average for privates right now is $32K. I am going to throw out two names based on your requirement above: Cedarville U: https://www.cedarville.edu/
And Lipscomb University: https://www.lipscomb.edu/
Sounds like your daughter is pre-med? I know two solid kids that went to these schools from the RDU area. One is in med school and the other is treating orphans in Africa and will surely get into med school. Forget prestige. Go somewhere where your daughter will be the top student and the school provides adequate rigor to ace the MCAT but not too much rigor (hello UNC).
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