Chris Petersen seems to be at the top of many peoples' lists here, but I'm extremely skeptical of him. Maybe it's not totally fair, but take a look at the *OTHER* Boise State coaches that leave Boise.
Dirk Koetter. Fantastic at Boise State. Went 10-3 and 10-2 in his 2nd and 3rd seasons at BSU. Was the coach that first ignited Boise State's spectacular run. He took at job at Arizona State and was OK. Went 40-34 there in six seasons. While he wasn't a failure at ASU, he wasn't a wild success like he was at Boise.
Dan Hawkins. Hawkins was an assistant under Koetter. He came in and took the program to even greater heights. Hawkins went 12-1, 13-1, and 11-1 in his 2nd, 3rd, and 4th seasons at BSU. He left for Colorado after his 5th season, and proceeded to go 19-39 and guided Colorado to being the worst team in the entire Big 12.
Maybe there's something about Boise State. Maybe it's the administration / infrastructure there. Maybe Boise has stockpiled great coaches and competent people, and so long as they have a competent HC, they can win ball games. Don't forget that this was a great Division I-AA program at one point, as well. They only entered I-A in 1996.
Why is Chris Petersen any different than Dan Hawkins? Maybe Petersen could come to Knoxville and rebuild Tennessee, but what evidence is there of this? Why does everyone believe he's a great coach? Is it simply because Boise State has had good records under him?
I can't help but to think that success at Boise State is tied to a lot of factors and the head coach is only a small piece of the puzzle. For this reason, I view Chris Petersen as a terrible candidate for the UT job. Let's also not forget that recruiting in the US South is going to be totally different than being in the Mountain West. No evidence that Petersen can recruit Florida, Georgia, and South Carolina.
I'd put Petersen way down the list. He could turn out to be a great HC at some major program, but I think James Franklin, Dan Mullen, Charlie Strong, and Gary Patterson are all much more proven than Petersen when it comes to coaching in a place like the SEC.
I'm not saying Petersen would be a bad coach outside Boise. Merely that he's a huge risk. We have no evidence that he can turnaround a program. We have no evidence that he can win outside of Boise, which has produced winning teams almost regardless of who coaches there. No evidence that he could compete in the SEC. All we know is that when inserted into an already-excellent Boise State program, he continued to make the program excel.