So many colleges won’t necessarily have a directed program in this area, BUT most colleges will have a critical mass of coursework in these areas that you can take. For example, the Princeton sequence simply looks like a western civilization class in two parts: antiquity to the middle ages and then the middle ages to the modern era. But that’s how western civ classes are usually split up - I took a history course like that at my own college. And I went to a historically black college.
If you want classes about Western civilization and culture - by which they mostly mean European, primarily Greek + Roman -> British with a little bit of Italian (when you read Machiavelli), literature and culture pre-1600s and American and British literature and culture post-1600s - you can find that anywhere and make a sequence out of it.
On the other hand, there is something to be said about a school that creates a program and has dedicated program/faculty resources for it. The Great Books programs were things I was also thinking about. On that list @simba9 provided, Chicago, Notre Dame, Boston College and UT-Austin are excellent traditional colleges with special sequences in the humanities. St. John’s, Thomas Aquinas and Shimer are Great Books colleges - no majors, no minors, but everyone follows the same prescribed set of tutorials and readings in the Great Books that span across humanities, social sciences, the life/physical sciences and the arts.
One place you should totally consider is Columbia. The Core Curriculum is basically this: Literature Humanities (whose formal title is “Masterpieces of Western Literature and Philosophy”) and Contemporary Civilization are both two-semester sequences that focus on primarily Western literature and the social sciences. You round it out with Art and Music Humanities (tours of the Western canon in both areas - formally titled “Masterpieces of Western Art/Music”), Frontiers of Science (ditto, but approached from a humanistic standpoint, which most students don’t appreciate) and some other coursework (Global Core, foreign language requirement, writing course). I will also say that the Core at Columbia has made an effort to include the voices of women and non-white writers in their canon - they recently added Toni Morrison’s Song of Solomon and Jane Austen’s Pride and Prejudice to the reading list, and you’ll also read Du Bois, Wollstonecraft, Woolf, and Sappho. And as for Music and Art Hum, Columbia offers comparable classes in East Asian, Islamic, and African art.
And, oddly enough, colleges with strong traditions in the humanities and no core curricula - like Brown or Amherst - might help you make a specialized sequence in this area while still also forming a concentration.
Last thing - if you have a strong interest in the humanities, I strongly urge you to consider the library resources and holdings of any university you consider. When you visit, visit the library for sure.