Nashville is doable if you go through around mid morning or late at night. Like Atlanta rush hour can be a bear. Unlike Atlanta, there is a lot of curves and intersecting on and off ramps from other major highways.
If you want to avoid Atlanta, you can go south on 75 to Ga 20 and turn east. Follow that to Lawrenceville and 316. Head east on 316 to US 78, then 78 to Thomson and I-20 and then Augusta and on to Myrtle Beach. If Atlanta traffic doesn't bother you, then 75 south to the intersection with I-20 and then east. It will be shorter, but at times (rush hour, on Fridays and anytime when raining) it can be a bear if you are not familiar with the area.