The weather along the coast can be variable in the October or December time period. The usual weather is to have low clouds and possibly fog in the mornings, which typically burns off in the afternoon. It's not uncommon to have bright blue skies in the afternoons and a nice breeze. But.... if the jet stream shifts and California starts getting a chain of storms then you can have a week of rainy/ cloudy weather. The farther north you go near SF, the more likely the skies will be grey.
I've driven the coast road numerous times in the winter -- and its been usually pretty nice (usually the Xmas-New Years week). I do recall getting rain once, but it was intermittent showery and the blasts of sun between the clouds was quite dramatic lighting along Big Sur.
You can drive from Death Valley to SF in a day, but its a rather long day's drive. As mentioned elsewhere, the Tioga pass over the Sierras most probably will be closed by snow at that point, so your fastest route is around the southern end of the Sierras through the high desert to Bakersfield, and then up the central valley. That does give you the option of stopping at somewhere like Yosemite, or perhaps some of the agriculatural areas through the central valley. There's an amazing variety of crops grown in the central valley -- grapes (wine, eating or raisins), fruits of all types, nuts of all types, cotton, row crops of a large number, vegetables and etc. California Olive Oils are a very rapidly developing commodity and VERY good, as are California Rices. There's a place near Sacramento I've stopped at that had 20 different varieties of rice for sale, all grown in the central valley.
Most folks, including myself will recommend going inland up to SF and then back south towards LA along PCH through Big Sur. However... there is the option of cutting over via California 41 to come out at Paso Robles, and then over to PCH at Cambria. That takes you through the wine country near Paso Robles and gives you the best part of the PCH up through Big Sur. From SF its a day's drive back to LA via I-5 (the fastest route). That is an option, but not a recommended one.