If you're looking for souvenirs, try the Arts Centre (west end of Worcester Boulevard, next to Hagley Park and the Botanical Gardens). In the weekend you'll see lots of little stalls there selling interesting stuff. Cathedral Square also has a little weekend market. I don't think we have a "Farmers Market" like many American cities seem to.
For general shopping, try one of the malls (Westfield Riccarton, on Riccarton Road, isn't bad) or for less mass-market stuff, wander around High St or Colombo St in the city centre.
If you're after some groceries, try Pak'n'save: it's consistently cheaper than the other supermarkets, and the quality of the vegetables and meat (especially the fillet steak in the butchery) is pretty good.