Here ya go:
TDOT SmartWay map
Mouse over any incident/construction sign and it will tell you what is going on.
You can also take Briley Parkway (SR 155) as an outer loop to bypass downtown. It is either exit 42 or 43 off of I-24 on the north side of Nashville. Go west on Briley Parkway, to I-40. Then east on I-40 for a couple of miles, then take I-440 around to I-65 southbound.
There is currently some work on I-24 westbound, and some paving on I-440. But paving season will likely be over with before you come through. And of course avoid morning/afternoon rush hour if possible.