I'd give a serious look to Joe Brady. You have a young talented QB in McCarthy you need to groom and implementing a legitimate modern passing offense would be a great start to turning around a stale program.
There are plenty of good coaches out there. Just have to find one who fits.
Probably a bad idea to hire one that runs a gimmicky offense in a shitty conference (RichRod), a guy who is really nothing more than a cheerleader and doesn't wear a headset & doesn't have input on scheme (Hoke), or a guy who is clearly retarded and also thinks offensive football is stuck in 1989 (Harbaugh).
Plenty of good coaches out there. But in all honesty it starts with the AD. Need to find an AD who is all in on football and who has a track record of hiring successful head coaches.
I'd say Michigan State's AD done a heckuva job with Dantonio and Tucker. Maybe don't need to hire him, but pay him a consulting fee to help you find a head coach.