Does it ever make sense NOT to go to the most prestigious grad school you can get into? I'm a senior undergrad at a top-ish(say, top 15) math school. I'm a solid, not stellar, student. This year I'm taking the qualifying exam grad courses in algebra and analysis and have been taken aback by the "pressure cooker" atmosphere among grad students here. That is, even moreso than in the undergraduate program. 
If I'm self driven, could going to a "less prestigious" school afford me more space(I mean in a psychological sense) to produce a more solid contribution to math? By "less prestigious", I mean a school "ranked" significantly lower than the range of schools that I could comfortably get into. For me, "less prestigious" would be ranked around 40-60 on, say, USNews or NRC. 
My reasoning is that at such a school, I would be more able to learn the fundamentals at my own pace, as opposed to a pace dictated to me by the program. I know I want to do math, and I think my learning style may be better suited to going at my own pace. Thoughts?
 A: It's true the atmosphere of a school make a big difference.  Without knowing anything more, I would suggest applying to a variety of schools, then visit the schools you get into.  This will give you a much better sense of whether or not the school is a good fit for you than just the ranking.  I think after visiting, you should be able to narrow your choice down to a couple schools you like, and at that point, probably either would be a good choice.
Incidentally, I wrote some tips on visiting grad schools after I visited quite a few.  You might also check out the career advice section on Terry Tao's blog, though I'm not sure there's anything specific about choosing a grad school.
A: The pace issue is a misconception of yours. You will have to learn the graduate level mathematics as quickly as is necessary to begin your dissertation work if you are going to a PhD program. Essentially, you have to catch up to a century's worth of mathematics in a year and a half. So deal with it. 
But to answer the original question, what will be essential to your survival in grad school and beyond is your relationship with your PhD advisor. I have seen students from not top programs land better jobs because their advisors took the time and care to help their students, bring them to conferences, introduce them to others working in the field, help them select post-doc positions, etc. 
If you know the area in which you want to work, then you should select grad school based on that. If you are not sure, then you should select among the best to which you are admitted, and select an advisor based upon her area of expertise and her ability to get grad students into good schools. Also check out the social network among the grad students. Is it solid? Will others help you in your studies. 
Ultimately, what makes your dissertation great is your own creativity and your depth of thought, but all else being equal, a good advisor is as important as the school that she teaches at.
