Better graduate departments attract smarter graduate students . Those graduate students will be your TAs, at basically all the schools under discussion. You want a dumb TA, go ahead disregard the grad rankings.
Similarly, they attract more accomplished Profs, who can add the occasional tidbits from their research to jazz things up. It feels cool to be in a class taught by a Nobel Prize winner, or a future one, whether or not he/she actually teaches any better.
Meanwhile there are really no rankings for undergrad departments available to be substituted AFAIK.
OP wants rankings, these are the rankings that exist. Accept “trickle down theory” or else there is no answer.