As much as Ole Miss would love to have you visit, I must warn you there is really no such thing as 'driving the Mississippi'. There are 15-foot levees surrounding it, so you either drive through the Delta (which is great, if you do that, get Steve Cheseborough's book "Blues Traveling"), or you use water to travel on the big river.

I'd go through Texas to N.O. which is convenient driving and forces you to stop for Cajun food and music, then head up through Mississippi to Memphis and Tennessee. Which would require blowing off Arkansas. So decide if what is wanted is a taste of the blues and jazz or that hillbilly Arkie stuff which you can probably get done better in Tinsee. Not to start a range war or anything....