Check
TDOT SmartWay traffic before you head through.
Also coming in on I-24, you can get off at Exit 54 on to SR-155, Briley Parkway, (either north or east-bound, I don't know what the Briley signs say at that point.) It loops almost all the way around Nashville. You will cross I-40, and then get to I-65 at MM 90 on the north side of the city. Briley Parkway occasionally jams up but nothing like going through downtown.
For the least traffic, start around by 6 AM on weekdays at the latest. Next best is early to mid-day on a weekend. Avoid 3-8 PM on weekdays.