Try the Natchez Trace Parkway. End to end it's about 444 miles. B&B's, hotels and camping off the Trace available near by. Some or all camp areas on the Trace itself may be closed for Covid so check with the Park Rangers.
https://www.scenictrace.com/why-you-...trace-parkway/
https://www.natcheztracetravel.com/b...the-trace.html
There are only a couple areas where you have to worry about heavy motor traffic. One of them being around me in the Jackson MS area. From just NE of Ridgeland to SW of Clinton during morning, noon and evening motorist going to and from work, it's quite busy. But a 11 mile long bike trail paralleling it will let you bypass some of the worst part. But if you time it to miss the rush hours, it's not bad then.
How far you wanting to go? I know you said you didn't want trails, but there are rails to trails routes that are fairly nice and scenic too. And they are just about long enough (40 and some odd miles) for a decent slow day of traveling. Two are in my state and I've seen some others elsewhere that look interesting.
Tanglefoot Trail
https://www.longleaftrace.org/
Being old railroads, they don't have any hills to even consider hills. Just a 1.5 to maybe 2 % steady grade.