I like the Victoria Quarter, stylish shops housed in grade II listed buildings!
If food is your thing, visit the Leeds farmers market at Kirkgate in town.
1st and 3rd Sunday of the month 9am-2pm - lots of local producers, lots of game from all around the region. Worth a trip for a bunch of bargain bites
Kirkgate Market is interesting any time and there are now farmers' markets in Headingley and Oakwood one Saturday each a month.
Briggate is the place to go for non-food shopping.