If you are going through Nashville at other than rush hour, and especially not on Fridays, straight through on I40 works well. Just remember to stay in the middle lane as you will need to "keep right" and "keep left" frequently to stay on I40 and not end up on the wrong side of a split.
If you have to hit it at rush hour, I840 would be the recommendation but it will add 30-45 minutes to the drive.
As for Memphis, there really isn't a bypass or alternate route. Just don't drive through at peak times. And realize as you approach the city going westbound, it's a right exit to stay on I40. If you are going eastbound, it will be a left exit at the end of the circuitous path to stay on I40.
2017 LTV Unity