[impendia]

I second the advice to go to Berkeley.

I am a university professor and so have hopped around from place to place (undergrad, grad, postdoc, faculty) and have seen that different universities are very different from each other.

At some places you are held to high standards. At some places you are not. Moreover, the most important thing you can do is to be around intelligent and motivated people, and the best schools offer this.

My math students at Stanford got a much better education from me than my math students where I am now. Consider what variable I have just controlled for... and you will understand why I'm suggesting you go somewhere top-notch if you can.