Old Hernandez Road
I would recommend heading up to Mendocino NF. It's about 3hrs from San Jose; a haul, epic for a day-trip but not for an overnighter. Camp in the NF cheap or one of the many hot springs joints like Wilbur Hot Springs
If you are going to ride the County roads in Clear Creek then don't forget to enjoy the Panoche Valley and if you want to stay the night then Mercey Hot Springs
is nearby and a good spot. There are some other BLM areas nearby that could be explored just be forewarned that they have "closed" them to all 2-wheeled vehicles... patrols are vanishingly rare and I wonder if the ranger would give you a ticket (as the closure to one class of plated vehicle can't be defensible in court) but you should know - and then pretend you didn't!