I need to provide my employer the court that issued my certificate of naturalization. My certificate doesn't state anything about a court though, just the city Fairfax. Would this court be the one that issued my certificate?

Yes, the local Federal Court is the most likely place.

I doubt that the Fairfax courthouse issued your certificate because they are all state courts. Naturalizations are federal actions. You may have been sworn in the city of Fairfax. Just bring your certificate to the employer. Or call an immigration attorney. They will know immediately what to say. Attorney Deeba Anwari is a good resource for this. Chris