On your ride up the Natchez Trace, a couple of suggestions.
I can get you coordinates if you need them, but a Google search should bring up whatever information you need. Neither site is on the Trace, but they're nearby.
Quite a few people simply ride up the Natchez Trace in one day. Sure, it's possible, but you don't get to experience the Trace as it should be. As a road, I find it kind of boring. It's mostly flat. Not too curvy except for the northern section. Low speed limit.
Unlike the similar but different Blue Ridge Parkway, which was created for the sole purpose of putting the driver in scenic locations, the Natchez Trace, almost by very definition, goes through the flattest and sometimes least interesting areas. It started as a hiking path, so necessarily the travelers took the route of least resistance.
That's not a bad thing. The gem of the Natchez Trace is its history. Though you'll quickly get tired of stopping at every wayside attraction (there's a stop every couple miles or so, on average) you should do a bit of research and find those places in which you think you might be interested. Though probably almost nobody takes this long, I recommend a couple of days to fully appreciate the length of the Trace.