What time of the year are you going? If it's anytime other than June-August, you may have difficulty getting through the Sierra's.
You should also consider going through Death Valley. It doesn't take long to see stuff there.
Despite living in SoCal, I've never really spent much time in LA. There's just not a whole lot appealing there to me. That's all personal opinion though, but I'd rather spend extra time doing outdoorsey shit (Death Valley, extra time in Yosemite, or the PCH) than another day or two in LA.