Best route through Nashville?

Briley parkway is a definite no, too much stop and go.

I usually come thru from the East on I-40 and then North on I-24. Couple of times I came from the West I went through on I-40. Some screwy lane changes, but otherwise no big issues.

We go straight through on 40 but be alert to required lane changes to not go to I24, 440 and I65. It can be a mess during rush hour. I tell my wife to also be alert for need to change lanes as we go through. GPS is watched closely as well. If you are not familiar with Nashville, I suggest you look at Google Earth for their street view and aerial photos before you get to Nashville. That's what I did to get through Mobile, Alabama from Hwy 45 to east I 10 to Pensacola. You could take 840 around to the south of Nashville for a nice country drive but much longer.

Either of the interstates/loop...Nashville, compared to many cities, isn't that big or that congested.

You can alos take 840 from around Lebanon, to the south and come out near Dickson, and get back to I-40. South west section of 840 is very scenic. Traffic will be very minimal.

stay on 40 the 440 is not bad but still have lane changes

The new 840 is the best way to avoid the Nashville traffic and "which lane" syndrome. Biggest problem going through town or 440 is having to know which lane to be in and when.

Plus, very scenic as mentioned by Dr Quick.

The newly completed (Nov 2013) 840 is only 16 miles further than staying on I-40 thru downtown Nashville. Much of it is 70mph, and substantially less traffic, so it's six of one, half dozen of the other. If rush hour, definitely take 840, or if you're aware of any accidents, etc. Also very scenic, and intersects with Natchez Trace Parkway that goes to Jackson, Ms (thru Tupelo, if you're an Elvis fan), or if you are considering a more southern route west, ie I-20 or I-10.

Above may/may not be useful depending on your ultimate destination, where you planning Memphis or a different route west of Nashville?

Like edm3rd said, if near rush hour take 840.
If I were going through Nashville I always take 440 or Briley Parkway.

We just came through there a few days ago. Just get on I 40 and cruise. We took 40 from Holbrook AZ all the way to Ashevill NC and more than 90% of it was awesome. A few short rough sections and just a couple of short stretches of ongoing repairs. :C

Avoid rush hour morning and afternoon and Nashville is no problem.