Unsolicited Advice, Part Three: Choosing an Undergraduate School

In comments, JMG3Y asks, "Where should a smart science-oriented high school student with a breadth of interests go to college?" This deserves a much more careful answer, but time is precious, so consider this a rough draft of an answer, which people are welcome to amplify in the comments. (Past installments here and here. At some future date there will be an installment on "How to be a good graduate student.") In reality, colleges and universities are very different from each other, and each should be considered separately. Also in reality, any such institution is huge and multifaceted, and two people can have wildly divergent experiences at the same place. Furthermore, sticking again to reality, this is a question that depends mostly on the individual student, and for which there is no right answer. Being all that as it may, for purposes of exposition let's lump the possibilities into four ...