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Not surprisingly, Harvard has been in the NCAA basketball tourney the last 4-5 years in a row after a 50+ year hiatus. Now granted, they're likely not letting in illiterates like some programs (here's looking at you UNC! ) but those kids are nowhere near the academic caliber of a typical Harvard student.
The Ivies use a metric called the Academic Index to compare the academic credentials of athletes to non-athletes. Typically, these schools won't accept recruits with an AI that falls below one standard deviation from the AI of the overall student body.
The recruits probably aren't as accomplished when it comes to extracurriculars like research or academic competitions, but their standardized scores and GPAs should be comparable to the rest of the class.
Top universities have, as a whole, better students (meaning students who have higher levels of academic achievement on entry). That is the primary difference between the top universities and schools like USC or UCLA, which still have strong research departments but weaker student bodies. Cal State LA & Long Beach have lower levels of achievement than USC/UCLA, and are not nearly as strong in research.
Still, those schools do provide quality education, and are appropriate for a number of students.
A high achieving high school student would likely be well-served aiming for a school with a higher achieving student body.
This is generally true.
There is a fair bit of "sorting" that happens during college admissions. Ambitious, smart students tend to sort together at the top tier schools, less-ambition but smart students tend to end up at second-tier schools, less-smart, less ambitious at mediocre schools, etc. Of course there are exceptions to this general rule, but it's a fairly accurate way of understanding.
The benefits of the top tier schools are:
1) Other ambitious, smart students to compete with. This competition isn't always direct, but it provides a higher yardstick to measure yourself against. "Steel sharpens steel" as the saying goes. This also isn't always the best situation for some people. Some people do better as big fish in a medium-sized pool, so being somewhere where they are a small fish in a big pond may actually be detrimental to some people.
2) Exposure to cutting-edge ideas and events. Top tier schools have guest speakers of high caliber. They have research at the leading edge of their fields of study. They have alumni in important, influential positions. Students who can take advantage of those will benefit from them. Some students who can't take advantage of that won't benefit.
3) Higher standards overall. At top-tier schools everyone is held to the highest standards from the dean to the faculty on down. This translates into high expectations for students to meet, pushing them to excel.
4) Generally better facilities. Modern equipment, better equipment, more equipment.
5) Generally better scholarships/grants. Potentially less need to borrow to attend.
6) Better name-recognition among employers nationally and internationally. Sometimes this even translates into easier work visas if you want to work overseas. For example, Denmark gives you additional points toward a work visa if you graduate from certain top-tier schools.
One of our top students last year ended up at a smaller school in Oregon, which will not be named, because they offered him a generous scholarship. His family is not poor, but he must pay the entire bill for school and couldn't afford to attend the University of Washington, where he would otherwise be. Anyway, he complains that "no one studies" at his school, so its been difficult finding like minded, bright and driven friends to hang out with.
On the other hand, our top student is at an Ivy league school, studying more than she ever did in HS, and enjoying some of the benefits listed by emathias above.
With financial aid, it's also cheaper than her top picks on the west coast, an extra bonus.
One of our top students last year ended up at a smaller school in Oregon, which will not be named, because they offered him a generous scholarship. His family is not poor, but he must pay the entire bill for school and couldn't afford to attend the University of Washington, where he would otherwise be. Anyway, he complains that "no one studies" at his school, so its been difficult finding like minded, bright and driven friends to hang out with.
On the other hand, our top student is at an Ivy league school, studying more than she ever did in HS, and enjoying some of the benefits listed by emathias above.
With financial aid, it's also cheaper than her top picks on the west coast, an extra bonus.
The presence or absence of like "like minded, bright, and driven friends to hang out with" has to be critical in a college decision. Our DD could have attended an in state school for basically nothing given the package they offered, but after visiting and comparing the educational value, we decided that "free" (or almost so) carried to heavy a price due to the low academic standards and lack of drive among the student body. It would have dragged her down. We ended up deciding on an out of state school with much stronger academics and student achievement even though the price tag was much higher.
I don't know if a 1,2,3 ... ranking means much between number 1 and 25 or between 100 and 200, but there's a huge drop between 25 and 100. Maybe it would make more distinction to say "Top"; Average; Mediocre; Bottom than number rankings.
High ranking schools have better equipment for labs, science, technology, fine arts, performing arts. You don't have to share lab equipment and you have newer supplies in better condition. You don't have so many TAs teaching introductory courses. More sections of courses are offered so you aren't as likely to get stuck trying to follow the necessary sequence of courses in order to graduate in 4 years. Classes like labs, performing arts classes like ear training are smaller. You'll make connections for life. You can get sent to conferences paid by the school. More opportunities to meet the big shots in your potential field, as well as sophisticated international students who can be royalty. Working on one of the student-run Harvard publications is a much bigger deal than writing for the small underfunded local college newspaper/online journal.
In my living around the US, I found that in may locales, even in some states, that many of the local/state colleges were thought more highly of than many "higher" level schools. Now the "upper" level schools like Harvard, Yale, etc. were still held in the highest esteem.
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Now granted, they're likely not letting in illiterates like some programs (here's looking at you UNC! 
) but those kids are nowhere near the academic caliber of a typical Harvard student.
