JT can be crowded in November. The south part of the park is furthest from LA, and the least used. If car camping, stay at the Cottonwood campground. Mostly snowbirds who go to sleep at 8:00pm and astonomers who are quiet. There is a nice trail to Lost Palms Oasis. Crowded for the first couple of miles. Or you can drive to other areas.
Mead - lots of campgrounds. Take the dirt road to the Rim of Fire trailhead (get a topo map). Not a lot of trails in the area, but a nice hike to the Rim of Fire. If there was a recent rain, there is a slot canyon on the other side of the west ridge of the Rim. You will have to look at the topo and see what wash to hike. I can't remember the name, but it is too strenous for a day hike to climb over the ridge from the Rim of Fire, but there is a dirt road from the Rim of Fire trailhead to the wash.