With regards to shopping, Durham seems to be a typical mid-sized city.  There are some unique shopping areas like Brightleaf Square and 9th St.  New Hope Commons & Indigo Corners are recent editions with some large chain stores. 

15-501/University drive area:  A Target / Sam's club and some other large chains are in this area. 

Malls: 

The Streets at Southpointe is a fairly new, higher end (for the area) mall.  With several nice restaurants, a good movie theater, and quality anchor stores, this has become *the* mall in Durham.  Located at the very southern end of Durham, south of I-40, it is easily accessable from points east (Raleigh) and west (Chapel Hill).

A slightly older mall located off I-85 is Northgate mall it recently underwent a major renovation and now has a large cinema complex.

Check out this link for all the shopping areas in Durham.