So far, (and surprisingly), the University of Illinois has withstood the PC pressure to change the school's team name and mascot. Leave the Chief alone, NCAA.
The Chief is NOT a mascot, and I defy anyone to prove otherwise.
Illinois is derived from "iliniwok", apparently from the Algonquin term for "warriors" or "tribe of superior men". (Google is so much fun.) So is the state name offensive? If the state name isn't offensive, why should an Indian mascot for the flagship university in the state be offensive? What if the U of I has a few Native Americans enrolled? Is it OK then?
Being from Wisconsin, I always like the Rhinelander HS mascot -- the Hodag.
There's a bunch of mythological Indian beasties out there - maybe the schools that are facing this idiotic rule could change to one of them. When Marquette was dithering over a new name, I suggested the Piasa Bird, a legendary and fearsome creature of Indian lore described by Pere Marquette. Much more awe-inspiring than a golden eagle.