I don't see why Kentucky would be undesirable to Petrino. He had a lot of success in the state, and the east is softer than the west. If he takes them to bowl games, not only would he have job security but his name would come up for top tier positions. Consider how the east and the west stack up this year (5-4 Vandy is fourth in the East), even with the east being a bit better this year than the past couple years. On the other hand, if Kentucky wants to go to bowl games, they need a guy like Petrino.
At Kentucky, being middle of the pack of the SEC East would be considered good, but at Auburn being middle of the pack is not acceptable. All he'd really have to do at Kentucky, is get ahead of Missouri, and Vanderbilt, and I don't see any reason he can't have close to the level of success South Carolina has.
At Auburn, they won't accept being fourth in the SEC West on a regular basis, but they are well behind Alabama and LSU. Along with that, Texas A&M appears to be on the right track, and seem well ahead of Auburn as well. So, he has to jump in and accomplish more at Auburn, with more working against him.
Auburn is a top 30 school, but they are somewhere between a top tier job and a stepping stone. You don't go to Auburn to win national championships, but you don't move up from Auburn either. It's a dead end for head coaching careers. They also will fire you no matter what after one bad season.
Arkansas? I just don't see their reversing course with Petrino, just doesn't seem possible.
If the Tennessee job was up for grabs, I would think Petrino would prefer that, but I don't think UT has the need to take on any baggage. If he had that chance though, he should jump at it. The SEC East is softer, and he could reasonably expect to compete at the top there.
Strictly as a coach, I thought Petrino was one of the best in the SEC. I think you can argue that Saban, Miles, and Spurrier are better... but I don't think you can make a lot of convincing arguments after that. Yes, he's not a defensive guy, but he won at his last two stops. He's also not a great recruiter, but seriously... we know what Auburn would do if he was there. They have a higher salary cap for players and they'd use it. I don't know how well he'd do at Auburn, but I don't imagine he'd be completely running things either, which could work against him.