I'm an undergraduate studying math and will be applying to grad school in the future. The top graduate programs are MIT, Harvard, Stanford, Princeton, Berkeley and Chicago. However, I doubt I would be near the top of the class at these places (if I got admitted, that is). This could have a negative impact on my academic performance as I have always been near the top of my class during my undergrad.
I think I would do better academically at a slightly lower ranked place like Michigan, UCLA, Columbia, Yale, NYU (Courant) where I would be closer to the top of the class.
What do you think? Should I avoid applying to the top 6 graduate programs?