All the top schools are liberal. It is just a matter of degree.
I do worry about my daughter being in Durham. Crime is a concern. She needs to stay on campus and avoid the city.
Duke offers very little when it comes to advantages over public institutions like UNC these days. I know guys wedged in the hollers of Appalachia at tiny Methodist churches that have degrees from Duke. Where Duke excels is in its graduate schools. A graduate degree from Duke is like having the Holy Grail. I know a few of them. Anything medical/science/economics is winning the lottery
However, private school can bring the costs down to in-state levels. My son could have gone to most private schools in the country for what we pay to send him to Virginia Tech.