<p>I doubt that Harvard, Penn, Princeton, Yale and U of C vary significantly in their ‘liberalness’, by which I mean the likelihood that most students and most professors will share a basically progressive mindset and politics, and be pretty condescending about the presumed naivete of committed Christians. </p>
<p>At the same time, the more intellectually vibrant a university is, the more responsive people are likely to be to a student who is serious about their faith and able to engage in analysis and dialogue about their faith with their peers. In that sense, the intellectual vibrancy of U of C, Yale, Princeton, Harvard and Penn (my ordering reflects my judgement, based on my experiences only) are all likely to contribute to the existence of satisfying (although perhaps small) support groups of like-minded Christians.</p>
<p>For math and physics, Harvard, Princeton and U of C can’t be beat (I don’t actually know enuf about Harvey Mudd, maybe them too).</p>
<p>For music, Yale, Harvard, Princeton, U of C are at the top from his list. </p>
<p>Given those lists, and given that it’s (still) much easier to get in to U of C than Y H and P, it would be a mistake not to apply. Given that the music scene at Yale is the best there is for the activities you list, it would be a mistake not to apply.</p>