Sticking with the route you have mentioned I have a couple of recommendations.
Near Little Rock I would suggest you take a look at Maumelle Park which would not be far off I-40 (Northwest of the city). It is a big wooded park on the river yet not far from shopping. It would be a nice place to stay over for a few days.
Near Nashville I would suggest you take a look at Seven Points COE, not far south of the city.
If you are not committed to going to Nashville, you could vary your route by going across southern Tennessee. For example on US 64 through Lawrenceburg where there is David Crockett State Park.
From US 64 you could go on to Chattanooga, or cut up across state highways to I-40 near Crossville.
We did the latter in September of 2015. Actually we went up through Arkansas to cross the Mississippi near Dyersville, TN and then dropped down to Jackson and on to US 64. Certainly not the direct route, but we enjoyed it.