Bucky's BBQ is one of our favorites in Greenville and about 5 minutes off of 85.
1700 Roper Mountain Road, Greenville, SC 29615
Southern Fried Green Tomatoes is a meat and three style place.
1175 Woods Crossing Rd Greenville Sc 26607
I know Bucky's is closed on Sundays but I am not sure about SFGT.
Enjoy and Safe travels
I second the I-20 route; Greenville is too far north. But rather than stopping in Columbia, I suggest Aiken, SC. It's right about halfway on the drive, and has some great dining options. My favorite lunch spot is Stoplight Deli on route 19 (http://www.stoplightdeli.com/) but there are other, more upscale dining options all downtown wihtin 3-blocks of walking. Here's an old link with good insights: http://chowhound.chow.com/topics/412013. Just get off I-20 at route 19 and head south about 5-miles.
I like doing the back roads heading that way. Carolina Barbecue in New Ellenton (down 19 S from Aiken) is a favorite stop of mine. From there, I take 278 to Barnwell, then 64 to Walterboro and then to 17. Just don't get stopped by the cops in Olar.
The route may not make perfect sense for OP, but that's the way I go from Atlanta via I-20.
You'll save time if you cut out Greenville and cut across to 126 via Highway 8 (I think) through Pelzer. Or even the toll road just below Greenville. If you can wait until you get to Columbia, you could try Hudson's Smokehouse on Highway 378. I wouldn't be much off the track and is worth it. http://www.hudsonssmokehouse.com/