I looked at the Liberty Bowl. I had a hard time figuring out who owned it or whether it was a nonprofit. However, it has been in Memphis forever, is played at Memphis' stadium, and is run by Steve Ehrhart, a Memphis based businessman who is connected to all sorts of Memphis sports stuff. So it has more local flair than I imagine most of these places do. It's sponsored by AutoZone, a Memphis based business.
The Independence Bowl also has regional flair, as the stadium is owned by Shreveport Louisiana and as far as I can tell not much else goes on there.