Most any part as far as I can see. The thing is about one mile wide and five hundred miles long. There are a few little old towns off it that are interesting but after the first 50 miles the Trace is pretty much a repitition. Try the Tennessee end.
I agree with Carl. The Natchez Trace is quite pleasant but can get boring after a day or so. Most scenic highways offer a variety of scenery, but in my opinion the Natchez is flat & repetitious. The northern end, which gets into the Tennesee River/Lakes country, offers a bit more than the central and southern sections.