to mansi in post #8: obviously there are many different criteria to use, ans you should make your own criteria and researech these places by thoise to get a good fit for yourself.
an often used criterion is: numbers of phd grads per year (favors big places and places which attract good students).
also reputation amongst iother mathematicians as revealed by poll placement taken by AMS survey, but only every so many years, also favors places which are already famous, and fgreatly lags actual improvement or decline.
you should look i think for who is there in the area you favor, and how much money they have to support you in your work, and how much free time they give you to work as opposed to spending your time teaching (also faviors big rich places).
but you also need to know how many years they give you to graduate, how good and how friendly the other students are, for interaction. (obviously changes yearly but is influenced by tenor of the place as established by the department - are there student run seminars, do students have a say in things, do students get adequate, or ANY! training in teaching before being thrown in th classroom?)
I never got a single bit of teacher training before beginning to teach over 30 years ago.
if you can find it out you want to know how successful schools are at placing grads. that can depend on fame of school but also on energy and commitment of advisor. Phillip Griffiths now head of the IAS, used to be indefatigable in helping his (excellent) students get jobs after Berkeley grad school, phoning on their behalf, etc...
In the present day climate of declining american enrollments in math and attempts to increase them, there are sopecial programs like VIGRE that favor us citizens. some of these are at smaller places like may Iowa or Kansas, I forget, as well as UGA (until last year). These things affect support levels and also change yearly. ask what the commitment is for support, and how renewal is decided.
ask how many faculty have NSF or other grants to suport grad students? and what the university's own level of commitment is.