You can find local PlayStation 3 service centers in the United States by navigating to the Sony support site, clicking on the Repair link, and submitting the required information about the product. Alternately, you can obtain information on approved PS3 service centers from the store where you purchased it.
Before going in for repairs, check the Common Problems and Troubleshooting Information page on the support website. If you do need to go to the service center, you may be able to get your PS3 repaired or replaced free of charge if the problem is covered by your warranty. Repair shops that are not affiliated with the manufacturer do not provide warranty benefits and may be less reliable.