How about dropping by Little Rock, AR and take in the excellent Clinton library.
And a good place to stay over a couple of days is at Maumelle Park, a big wooded park on the river.
After that either go on up I-40 to West Memphis or, if you prefer non-freeway up US 67 through northeast Arkansas.
You could cross the river near Dyersburg, Tennessee, then US 51 to connect with the Purchase Parkway, one of the excellent Kentucky parkway system.
You could cross the Ohio at Henderson, KY/ Eveansville, IN. A great place to stay is the Audubon State Park near the river in Kentucky.
I could go on, but this is the part of the route I am personally familiar with, so I'll stop right here.
