It might be interesting to look at where my colleagues studied, to see where someone can end up after graduate school. This information is public on our web page so I am not speaking out of school here.
KU. (Ok, that's unusual, to work where you yourself got a PhD. That's exceptional.)
U of Wisconsin, Madison. (2) A good state university.
Indiana. (2) Another excellent "Big 10" School.
Cornell. Ivy League.
Pittsburgh. A good university with an exceptionally strong history in Latin American literature.
U of California, San Diego (2).
Yale. Another Ivy.
Stanford. (That's me.)
UC Santa Barbara. That's three total from the UC system.
Illinois. A fifth big-ten graduate.
So we could say that if you wanted to end up at KU, you would do well to study in California at a good UC system or at a good big-10 school. If you looked at where our graduates are going, you would find a larger variety of schools, since everyone gets their PhD at a research university (almost by definition) and not every graduate of a research institution ends up at one. Thus the general trend is downward, in terms of prestige: some people move more or less laterally, from a Michigan to an Indiana, or from a Wisconsin to an Illinois, but many students end up at a SLAC, a regional comprehensive MA-granting school, or elsewhere off the tenure track completely. The Ivy-league mostly hires only Ivy-leaguers or those from the best private and the very best public institutions, but the Ivy League cannot hire more than a small fraction of its own graduates, since those departments tend to be small anyway.