For Stem Cell research these are the top universities:
Harvard, UCSF, Stanford, UCLA, MIT (especially for Rudolf Jaenisch), Cambridge (for Austin Smith)
Columbia and Yale have new stem cell centers and so they have up and coming stem cell PIs.
Hope this helps!
We do have an advantage over international students who do not have a bachelor's degree from the US but when it comes to funding, we are still in that pool of international students, and that prevents graduate programs from accepting us