It is the time of year in the US that high school students have found out what schools have accepted them and now have to decide where to spend the next four years. Maybe because I am of that age, but I find myself talking more to students and parents about what school they should choose.
So let's assume you are a high school student who knows they will eventually want to get a Ph.D. in computational complexity or perhaps some other math-related topic. Where to go to school? Depends much on your personality and your choices.
The Elites (examples: Princeton, Harvard, Stanford, Yale): Many rich kids who feel entitled so you can get good grades without working hard. But you can also take advantage of great professors and some challenging courses and research opportunities if you are up to the challenge.
Intense Schools (MIT, Caltech, U. Chicago): Here you have to work hard for your grades against other very strong students in challenging courses. You won't have a better math/science education anywhere else but these schools won't give you as broad a social experience.
Broad Private Schools (Cornell, Northwestern): Here I have biases having gone to Cornell undergrad and now teach at Northwestern. Fine math and science programs not quite as strong as the above but more than made up by experiencing an undergraduate life with smart students across a wide spectrum of disciplines. Many a theorist got their start as a Cornell undergrad.
Liberal Arts Schools (Williams, Wesleyan, Harvey Mudd): You don't get the large research programs but instead have very good profs who focus on undergrad teaching. This is the easiest way to get involved in research as an undergrad.
Big State Schools (Illinois, U. California, Michigan, Wisconsin): You get a real mix of students from athletes to partiers to really smart kids looking to save a few dollars. You can certainly get a great math and science education. But you'll have to work hard when many of your fellow students may not be.
General advice: Doesn't really matter that much where you go, as long as you work hard you will succeed. Above all enjoy your undergrad days for they will be the best times of your life.