The main shopping area is formed by Aleksandrovska Str. and Bogoridi Str. and all the streets leading off from them. Your best bet is to wander around the central and back streets and see what you come across.
Most shops are open from about 10am to 7 pm on weekdays and till 1 pm on Saturdays, though there are many 24-hour food shops in the center and private shops which now open on Saturday afternoons.
Some of the new and bigger shops now accept credit cards but in general you still need to carry cash.