I am always amazed at the misinformation that floats around here on college rankings and scholarships. There is an entire industry based around ranking schools that basically get it fight US News and Forbes are the tip of the iceberg. The tier that a school is in ie, top 10, 10-20 etc. is more important than the specific rank, as those results shuffle around a bit each year. The generally accepted top schools are (ha ha in no particular order)
Harvard, Yale, Princeton, Stanford, MIT & Cal Tech at the university level and Williams, Amherst and Swarthmore at the small liberal arts college level.
There are many fine institutions like the rest of the Ivies, U Chicago, Cal Berkeley, Armed Forces etc that may be just as good or better, but the generally accepted list is the one above. One can look at the data for acceptance rate, grades and test scores, and yield (this is what% of accepted students choose to attend) to get a feel for which school is particularly popular at any given time. Stanford does have a few advantages over the rest of the list - 1) climate, 2) access to Silicon Valley and 3)PAC 12 sports program, which make it an attractive option for many - and certainly under consideration as the best university in the US.
Obviously the teaching, research opportunities and available funding for projects makes these schools amazing, but even moreso, it is the quality of the student body. If your peer group in the classroom are all hardworking, motivated geniuses, that tends to push and drag along everyone to step up and perform at the same level.
A key point made above also noted the difference between undergrad and grad programs. Undergrad inside a big university can be daunting, and best serves the type of student who is a go getter - can sort of bust through red tape and complications and demand that they get the best education for their money. Otherwise it can be easy to get a bit lost and kind of muddle through, which is sad at a top school. The small liberal arts colleges are more like giant high schools, with only about 500 kids per class, and very few (sometimes none) grad programs. This makes access to profs and the support structure much easier, so in theory there are less distractions and roadblocks toward getting an education.
Financial Aid and scholarships
Only Stanford of the above top schools offer athletic scholarships. All of the others do fully fund 100% of financial need. Currently, if your family makes $100,000 or less annually, you basically get a free need-based scholarship to any of these schools if you are accepted there, and keep a GPA over 2.0 during your time there.
In one of the more shocking college statistics, over half of college applicants with high school GPA over 3.5 and classic SATs over 1300 do not understand how the financial aid system works and never take advantage of the available money. An organisation called Questbridge is trying to do something about this by reaching out to high schools to find these lower income kids, and then pairing them up with the top colleges - it's worth a look at their site, as in great detail it explains all of what I just touch on here.
Admissions Favoritism
What a coach can do when the scholarships run out, or at a non scholarship school is to present their list of recruited athletes to the admissions department. Say the school's average SAT is 1400 - each coach and team will receive a certain number of exceptions, where the school will accept lower results and still admit. It might be 20 per year for football and 7 per year for track/cross country etc. and just how low the academic performance can go varies at each school. It's pretty normal across the iveys for football players with 1200 SATs to get in. I'm aware of a few instances of 1000-1100, but I'm not sure if anything under 1000 would cut it. The key is that the athlete must be on the physical specific list of "tipped athletes", it's not just based on your college app. So a 4:20/9:30 kid with 1200 SAT who visited the school, met the coach and gets on the "tipped athlete list" will get in, while a 4:10 kid with a 1300 SAT, who is not specifically supported by the coach may not get in.
Just how far a school is willing to lower the standard for athletes is pretty interesting. Duke, Northwestern, Vanderbilt, Rice, Notre Dame, USC and CAL all have very demanding stats for general admissions, but still manage to field competitive D1 athletic teams. Go below this group to the standard D1 university and basically the bare minimum college entrance requirement will be OK for an athlete rather than just an adjustment to the normal requirement.
At the top schools the same process for "tipping" an athlete to admissions also exists for areas like chorus, band, theatre, some specific science departments, and for legacies - relationships with alumni, faculty etc, - and big donors. A school has to make sure that all the programs and facilities get used, and they do give advantages to relatives of alumni and big donors. Most of these admits come in the early decision process.
So in summary, Stanford is an excellent university...if your family makes less than $100k a year, there is a lot of financial aid floating around for top students, and an athlete can achieve 1 of 2 things at a college 1- earn an athletic scholarship, or 2- use your athletic performance to get accepted to a stronger academic school then your GPA and SATs might qualify you for.