Based on the below driving distances from all schools, holding the tournament in Greenville would make the most sense. I still think Gwinnett (Atlanta) wouldn't be a bad option given that most of the driving miles are by interstate.
Traveling Distances:
Asheville:
ETSU - 61 miles
Furman - 63 miles
UNCG - 173 miles
Wofford - 70 miles
Citadel - 268 miles
UTC - 219 miles
Western Carolina - 53 miles
Samford - 372 miles
Mercer - 248 miles
VMI - 285 miles
TOTAL: 1,812 miles
Greenville:
ETSU - 121 miles
Furman - 0 miles
UNCG - 189 miles
Wofford - 34 miles
Citadel - 213 miles
UTC - 250 miles
Western Carolina - 105 miles
Samford - 292 miles
Mercer - 186 miles
VMI - 345 miles
TOTAL: 1,735 miles
Gwinnett (Atlanta)
ETSU - 240 miles
Furman - 119 miles
UNCG - 306 miles
Wofford - 147 miles
Citadel - 330 miles
UTC - 132 miles
Western Carolina - 128 miles
Samford - 175 miles
Mercer - 107 miles
VMI - 449 miles
TOTAL: 2,133 miles