Peachtree in Atlanta and Old Town in Winston-Salem both have pure bent greens. Peachtree's are relatively new in last few years, I believe. Perhaps other members will know the type(s), but if not I bet you can call the clubs themselves and ask.
Peachtree is one of the finest conditioned courses you will find anywhere, and the whole experience there is off the charts (great history, great caddies, great terrain, etc.).
p.s. Most GCA'ers wouldn't like Peachtree, though. Green fairways, smooth greens, and trees (heavens, no!).