you are talking about graduate school though. The OP still needs to graduate high school and then get a BA or BS before going on to grad school. I like the idea of a small liberal arts college mentioned above. It can be the best form of higher education in today's world. Many schools like Oberlin or Amherst are more highly respected than the Ivies.
This is absolutely bogus. If you are at all serious about any subject, you will be taking graduate courses at the end of your undergrad career. The schools with the best graduate departments are the top universities that everyone has heard of.
Obviously, introductory courses are pretty much the same everywhere, but that isn't the measure of a good education.
I went to UVA and double majored in math and physics. The math department isn't particularly good, I think it's ranked 35th or so in the set of all math grad schools. I took a bunch of grad courses, 1.5 years worth, and I thought I was hot ****. Then I went to the University of Maryland, which is ranked 15th, and saw another level. The same level of classes were much more rigorous, harder, and covered more topics. I even had a taste of what Princeton-level grad math was like because one of my professors was snatched away from Princeton and didn't change the lectures. The contrast from UVA was completely apparent.
Incidentally, the hardest I ever worked at UVA was a philosophy class where, surprise!, UVA is highly ranked.
My point being, the top-ranked schools really are that good. It is important to get the subject right (for example, UVA is good in soft-sciences but not nearly as good in the hard sciences), but for the most part you cannot go wrong going to Harvard and the like.
Going back to the OP, I'm sorry to say but in this day and age it's really hard to get into top schools. I see people all the time with 4.0s, top SAT scores, and activities out the wazoo not get into top school. It's mostly a problem of grade inflation, making it much more difficult to separate yourself from your peers. The only way to counteract it is to specialize in high school (research, etc) but I think that's a crap thing to be forced to do in high school.
As a mild contradiction to what I said earlier, non-top schools generally
aren't bad. They aren't as good, but you can get a great education at a school you've never heard of. For my subject, UVA was a non-top school, but I don't really have any regrets going there because it got me into a good grad school.