I would look online for <brand name> 维修 place first. I would expect to pay a lot for any original brand (原装) parts and 20-50% of that cost for a generic replacement. For a phone, I would look for places near Taisheng Nan Lu rather than computer street.
Would also pick somewhere where I can see the technicians working and can see they have a clue what they are doing. If they have dirty or badly lit workstations covered with piles of dusty circuit boards, or if it is a screen problem and they say they have to take the phone/computer apart to see what kind of part they need, I would leave.