In Arkansas, I would suggest the Hemingway-Pfeiffer Museum in Piggott (
link). The museum is a house that belonged to his wife's family and he wrote a portion of "A Farewell to Arms" there. To get there, you could travel up the Crowley's Ridge Scenic Parkway (
link) starting in Helena-West Helena, Arkansas which has a history with blues and early rock and roll.
As far as restaurants, I would suggest the following:
Kelly's Restaurant (family style) - Junction of SH 1 North & US 64 in Wynne
Woody's BBQ - Junction of SH 14 & US 49 (in a camper behind the gas station) in Waldenburg (open I think W, Th, F & S only)
Bonnie's Place (family style) - on the town square in Piggott
If you wind up straying to the west of the Mississippi, I would suggest Craig's BBQ on US 70 in DeValls Bluff. No trip to Craig's is complete without crossing the highway and going to the pie shop afterwards.... Both have been there for at least 50 years....
Other restaurants to consider would be Doe's in Greenville (steaks sold by the pound and great tamales) and Jim Neely's Interstate BBQ in Memphis...
If you want to stay as close to the river as possible, the Great River Road would be a possibility (
link)...
I hope these suggestions help...