I'm hoping you get into Princeton and Stanford at this point just so you'll have a clean sweep.
I like your way of thinking! And I am happy to report that I did get into Stanford and Princeton.
I am seriously considering Stanford, Columbia, Michigan and Austin at this point, though I have yet to visit Stanford and Austin. There are so many great things about each of the schools that I decided to proceed by exclusion:
MIT and Princeton's graduate curriculum is not ideal for a liberal arts college student like me. (They assume that incoming graduate students have already had all of the core math courses and are ready to start doing research, which I am not.) Their graduate students seem to be under an intense amount of pressure and many have a hard time coping.
Cornell has the opposite problem - too little pressure. The graduate students described their graduate years as a "5-year-long vacation." I had the impression that many grad students weren't all that serious about their academics, and the department lets them get away with it. I think it'd prefer a more committed atmosphere.
Berkeley has atmosphere, location and an amazing funding offer going for it, but their geometry-topology group is not as strong as it used to be. And I didn't mesh with a good percentage of the faculty who are left.
To be honest, I hope that I will fall into love with Stanford when I visit next week. It would be incredibly painful to decline the big name schools to attend a "lower-ranked" one.