It seems everyone is ignoring your constraint, "driving distance from SF." But your constraint depends on how much driving you want to do and how much you want to pay also comes into play.
With a few hours drive North, you've got Humboldt, Mendocino, Marin, and other charming coastal towns. With a few hours East you have Tahoe and plenty of other places with snow this time of year. With up to a few hours South, you have Half Moon Bay, Davenport, Santa Cruz, Moss Landing, Monterey, Carmel, Moro Bay, Los Osos, Avila Beach, Pismo Beach, Santa Barbara, and more along the coast.
Due to the seasonal movements of the coastal cloud layer, some places on the cost actually have nicer weather during the winter than during the summer. Mendocino, Pacifica, Morro Bay, and (Northern) Santa Barbara are like this. Avila Beach is a strange anomaly and it is often nice year-round.
If you want mountains but no snow, there are lots of little places for retreats in the coastal mountain range that runs from SF down to SLO. Some are closer, and some are farther, but all are beautiful. The down-side is "fast" connectivity, but you can often solve that with phone tethering.
Your best bet is to search through AirBnB and similar sites.