Honestly if you’re a libertarian you’ll be fine at pretty much every top university. Students at the Ivies, Stanford, Georgetown, Chicago-- are happy to have spirited, civil, passionate debates about all of the issues near and dear to the hearts of libertarians. Conservative scholars are everywhere from Penn and Harvard to Chicago and Princeton. Chicago is actually pretty famous for the conservative professors they’ve employed (think Antonin Scalia) and their more conservative than average student body.
And think about some of the elite universities that conservative/republican leaders have graduated from: Ted Cruz is Princeton and Harvard, John Huntsman Jr. (former governor of the most genuinely conservative state, Utah) is Penn, Samuel Alito is Princeton and Yale, Clarence Thomas is Yale, Gorsuch is Columbia and Harvard, Frank Luntz is Penn, Scalia was Georgetown and Harvard, William F. Buckley was a Yale man, Ann Coulter is Cornell and Michigan Law (which is a top law school that genuinely rivals the elite privates), The Bush family is a Yale family, Mitt Romney went to Harvard for grad school, Bobby Jindal even went to Brown!, Rob Portman went to Dartmouth and Michigan Law, Justin Amash also went to Michigan Law, the President went to Penn, and the list goes on and on.
My point is not that these institutions are amazing at producing conservatives/republicans but rather that conservatives/republicans can thrive at all of these institutions, get amazing educations, and then use those outstanding educations to create the changes they want to see in the world.
Don’t be afraid of top colleges because of your political leanings. These universities need and welcome diverse opinions in order for their students and professors to truly thrive. And don’t be fooled into thinking that state schools in conservative states are going to be super conservative-- institutions of higher education outside of the religious universities you mentioned are going to be left leaning. But if you think it’s important to have the future leaders of tomorrow exposed to conservative ideologies during their educations, then you shouldn’t let the majority of liberals scare you off!