Uvas Canyon County Park
Getting there: From San Jose it took me about 40 minutes. The road is windy, narrow, and not for the car sick. Be prepared to pay $6 for parking.
Campsites: The campsites are nicely maintained. Plenty of area to pitch a tent, all the sites have a BBQ, fire pit, and picnic table. The sites are close together to maybe bring ear plugs in case you have loud neighbors.
The Park: Really pretty, really small. I would say in 1 full day you can explore 100% of this park. No need to make an entire weekend out of this place when you can do all of the pretty stuff in just a few hours.
What to do: Go see the waterfalls. With the current California drought all of the falls were at little more than a trickle but still something to see. To hike to each fall it's about 6ish miles with just a few hundred feet of total elevation gain. The trails are large and well defined for an very entry level experience.