Before there was a My Morning Jacket or Kings of Leon, there was The Band. 
The Band is considered to be one of the pivotal Southern rock bands, but they resided in Woodstock, NY. They do have Southern cred though, as drummer/singer Levon Helm is from Arkansas. While these guys spent 10 years playing unnoticed in bars in the 60s, they amassed a following which included Bob Dylan, who chose them to be his backing band; together, they wrote many songs. The Band then put out 2 genius albums, Music From Big Pink and the self-titled 2nd record, The Band. My favorite thing about them, aside from their complex and amazing songwriting, is their musical diversity. They had 3 singers and each member was incredibly skilled at their instrument so you never knew what combination you’re going to get, but it was always going to be of the highest quality. Martin Scorsese made a documentary about them called The Last Waltz, which I suggest watching if you like what you hear.
This video is of The Band playing “King Harvest Will Surely Come” + “Long Black Veil,” two great songs from their self-titled record.