Assuming you're going for the most direct, easy-to-drive route, Donna is spot on. I would offer the suggestion that the Little-Rock to St. Louis stretch could be done on US-67. This routing is fewer miles (about the same driving time), and would get you off the slab for awhile and would give you some nice views of the eastern Ozarks. You could even sneak in a stop to Taum Sauk Mountain - Missouri's state highpoint. Little Rock is still your mid-point as far as accommodations. I like Holiday Inn Express for rates and decent breakfast; your results may vary.

On the other hand, if you want to turn this into a 3-day touring road trip, I'd recommend taking portions of the Great River Road between Natchez, LA and St. Louis. US-65 and MS-1 will take you to Memphis, where you can either get on I-55 for the quick road or meander up the western Tennessee roads to the Kentucky Knob and take the Dorena-Hickman Ferry across the Mississippi River. From Missouri, MO-77 and US-62 will get you to Cairo, where there's a nice state park at the confluence of the Ohio and Mississippi Rivers, and IL-3 will take you to the St. Louis beltway. With this routing, your stops are Tallulah, LA, and Dyersburg, TN.