I am a college professor and I have taught at Chapel Hill, and have friends at Duke math dept, and my kids went to the TIP summer program for the gifted.
The following is the list of math faculty at Duke:
* Pankaj K Agarwal, Earl D. McLean, Jr., Professor (primary appt: Computer Science)
* William K Allard
* J. Thomas Beale
* Hubert L. Bray
* Robert L Bryant, J. M. Kreps Professor
* Herbert Edelsbrunner, Arts & Sciences Professor (primary appt: Computer Science)
* Richard M Hain, Chair
* John Harer, Vice Provost for Academic Affairs
* Harold Layton
* David R Morrison, James B. Duke Professor (joint with Physics)
* William L Pardon
* Arlie O Petters, (joint with Physics)
* Michael C Reed, Bishop-MacDermott Family Professor of Mathematics
* Donald Rose, (primary appt: Computer Science)
* Leslie D Saper
* David G Schaeffer, James B. Duke Professor
* Chad Schoen
* Mark A Stern, Associate Chair
* John Trangenstein, (joint with Civil and Environmental Engineering)
* Stephanos Venakides
* Xin Zhou
I personally know Robert Bryant, Dick Hain, and David Morrison and they are all superb both as researchers and teachers.
I recommend Duke to you highly in terms of academic quality of math faculty and their commitment to and skill in teaching.
Of course I myself may still be a halfwit, but the advice is free and truthful. Go see thopse guys and introduce yourself. See what you think of them, sit in on a class or three, especially from the ones I named.
I know a couple others less well, such as Chad Schoen and John Harer, and have very high opinions of their research credentials, but cannot recall seeing them teach.
I am from Nashville myself.