I know this is an old thread, but just for future reference:
Levy's - local department store with high end clothing. Zegna, Brioni, Ferragamo, etc. Across from the Green Hills Mall.
J. Michael's - men's clothing store. Talbott, AE, Polo, Alden, Bills Khakis. On West End, right next to the Vanderbilt campus.
The Oxford Shop - Bills, Talbott, etc. Down the street from the Green Hills Mall.
The best barbecue will be further west on I-40 in Memphis, but you should try Mary's Pit Bar-B-Que (1106 Jefferson St.) in Nashville. I also recommend Prince's Hot Chicken Shack (123 Ewing Dr.) for the best and hottest fried chicken you'll ever have.