<p>Tboyle- if you’re at the USAMO level- you should strongly consider MIT/Harvard then Caltech then maybe Chicago, Princeton, Stanford, Columbia, NYU- Courant etc. Among the LACs, I’ve heard good things about Swarthmore and if you exhaust classes there you can go to Penn. Also Noam Elkies went to Columbia (and Ciprian Manolescu and Ovidiu Savin both teach there so you could have some of the all time greats as potential mentors.)</p>
<p>If you’re CA in-state you should definitely go to UCB (I think three Fields medalists) or UCLA (Tao and the applied math center)</p>