Hello and welcome to the RTA forums !

As pointed out heading South on the PCH has the advantage of the Ocean views and pull outs being on your side of the road.

Starting from SF I would head to Yosemite [an amazing place] and spend a night and then head towards Monterey for another. The following day drive around Big Sur and look to stop over in Cambria, Cayucos or Morro Bay before continuing to LA.

The thing is with just 6 days, and say you want to have 2 in SF and 2 in LA sight seeing, with your 2 remaining days it might be a case of deciding between the coastal route or going to Yosemite and taking the faster inland route to LA.