If you're a high-performing high school senior from a non-affluent background, I can guarantee you've got a big dilemma coming your way: do you choose a college because it's affordable, or because it's your dream school?
You'll quickly find that a lot of the literature on this topic tends to bolster the value side of the debate--rightly so, given the pervasiveness of the student loan crisis.
The debt crisis has engendered a need to quantify American higher education: to examine cost, graduate earning potential, and financial aid packages, and to prize these things more than prestige, alumni networks, and the strength of campus recruitment.
As somebody who chose to go with prestige over value, I can tell you that this line of thinking, though extremely merited, becomes problematic when taken as absolute law. Your college experience is debatably the most formative four years of your life--you're fooling yourself if you think it's reducible to a series of numbers.
If you can afford to attend a prestigious school while only taking on a small or middling amount of debt, then I think you have a valid case to forego financial prudence and chase a dream. Though you'll take on student loans, debatably, these three things (among others) could make the debt worthwhile. For the sake of staying grounded, I've avoided the "fluffy" (though still important!) factors such as campus feel, social life, and extracurricular activities.
1). More Exposure to Diversity
High-powered schools attract students from across the globe, students that will ultimately look, act, and think differently than you. Coming into contact with these people and the diverse ideologies they proscribe to will do wonders for your own outlook on life. You'll be forced to examine issues differently, question your values, and defend your beliefs; these things will make you a better thinker, and ultimately, a better person.
Less prestigious schools attract some diversity, but not nearly as much as a renowned school. You may notice that groups of students from your high school are going to the same colleges in droves. If you can, avoid this at all costs: it's going to be much more difficult to meet different people when you're surrounded by so much familiarity. The critical thinking skills you develop from living in a diverse environment will serve you for the rest of your life, and will be a significant factor in determining what your future career looks like.
2). Stronger Job Recruiting
Simply stated: you'll have an easier time finding job opportunities coming out of a well-known school. Tufts receives an array of employers every year specifically seeking to hire its graduates. The existence of this program allowed me to secure a job well before graduation--with a BA in English, no less.
There isn't a recruiting program in this country that doesn't have an idea of which schools it's targeting for new hires. Generally speaking, those schools just tend to be the ones that are higher up in the rankings. To test this theory, take a look at your potential school's annual career fair roster. Are they attracting a lot of companies, and are those companies in the industry you might potentially want to work in?
An important note on this: notice I said "easier to find opportunities" rather than "get a job." Do not make the mistake of thinking a high-powered degree guarantees you a job--you will be sorely disappointed. The things you do at school, be that a prestigious school or not, are what will get you hired. A renowned school will just tend to have more opportunities for you to be discovered.
3). Powerful Alumni Networks
How do those companies decide which career fairs to attend? A school's prestige definitely factors in, but so do the opinions of the people who already work at said company. Where's the most logical place for those employees to suggest? The place they went to school, of course.
Research estimates that 60-80% of all jobs are obtained through a personal connection of some kind. Going to the same college as somebody is the perfect gateway to starting a professional relationship, something that could very easily become a job opportunity when needed.
Generally the most prestigious schools are the ones that have been around for the longest. Longer existence=more generations of alumni, and more time to hammer out a set of values to be instilled across a student body. There's a reason these "old boys' clubs" form, and it's not just to hang out with a group of like-minded people.