Greenville, not Greensboro. If you drive towards Greensoboro, you're in for a surprise. Downtown Greenville is actually quite nice.
Atlanta traffic is definitely bad. If you leave BMW at 3 or 4, you'll be there in time to miss most of it and be going against traffic into the city. What are you looking to do in Atlanta? Just get dinner? What kind of stuff do you like?
The easy choice is Buckhead or the Brookhaven/Perimeter area. You do not want to stop off of I-20... just... skip that until you are outside of the city. Atlanta is a lot like Houston or Dallas, huge and sprawling.
I've driven that exact route via 20 and it's not that exciting. Birmingham has some good points. Vicksburg has some great historical sites. A lot of the towns along the way are pretty small. I've stayed overnight in Meridian and it was just a dot on the map. Driving over the Mississipppi is cool. I've flown over it hundreds of times, but only driven over it maybe 5-10 times. It's really big.
I would almost be tempted to drive up to the Blue Ridge Pkwy or just into the mountains since you are so close. They are very beautiful. It would add another day, but a very pretty one especially if you aren't used to seeing mountains.