Depends on what you mean by local. The best matches for what you're talking about are:
Button Willow
Willow Springs
I don't know about either of these places, but Infineon up north has an annual pace that allows you to run on (I think) Fridays that aren't race weekends. However, your car has to be race prepped (cage, fire, etc.).
There's also AutoX events at Fontana Speedway from time to time I think. You might want to consider (as I have) Corvette Super Sport, which is VERY local to us and frequently organizes cruises as well as joint track days with the Porsche guys, etc.
http://www.corvettesupersports.com/