If you are looking for getting birth certificate(s) for your new born, the LAX Courthouse is the nearest one to the South Bay area. I recently went there for my son's birth certificates and to my surprise, was in and out of the building in less than 20 minutes.

They have metered parking spots around the building and you have to go through a security check (like Airports) to enter the elevators (go to 6th floor for birth certificate). The office have forms that needs some basic information about the newborn (city, name, month's maiden, birthday, and number of copies) and you'll have to show your I.D. for verification.

Make sure you carry your checkbook or carry enough cash as they don't accept Credit or Debit cards. When I went, the fees for a single copy of Birth Certificate was $17.

I went on a weekday at 10:00am and there was only a couple of people waiting in the line, so the entire process was very smooth and quick for me.