I know Stanford attracts some conservative students because of the Hoover Institution. I also had a very religious and conservative colleague who was thrilled that his daughter decided to go to the University of Dayton. It’s affiliated with the Catholic Church, though I don’t think it’s particularly religious.
BTW - what’s your current major at USC? I got an engineering degree at USC years ago, and while I can imagine a political discussion being initiated by a professor in certain courses, it’s hard (though not impossible) to see an engineering professor starting a political discussion. And don’t forget, Professor Schwarzenegger runs a policy institute there, as does Dan Schnur, who was a well-known Republican operative in California before ran for California Secretary of State.