Packsaddle Cave is near Kern River and Lake Isabella.
It’s a 5 mile out and back trail that can be done as a morning hike if you are visiting Kern River, Lake Isabella, or Sequoia National Forest.
My suggestion would be camp near Kern River, hike to the cave in the morning, and do a late afternoon hike at Trail of 100 giants in Sequoia National Forest.
The Cave itself is small enough that you won’t get lost but big enough to be interesting.
Note: I’ve seen people make comments about ticks in the area. While I didn’t see any on the trail, they are certainly in the area. A fellow camper found one in their tent.