There are lots of camping options besides the ones here & where the trail work is may determine where you camp.
Here are some suggestions

Near Lake Isabella for Spring & Fall Trail Appreciation Days

BEST OPTION
You can camp for free on the BLM land in Keyesville. Take 178 to the Lake Isabella exit & take 155 towards Kernville, Go up a hill & down a hill & then across a bridge over the Kern River, look for the immediate left & drive up the Keyesville Road about 1 mile to a parking area with a bathroom on your left. You can camp anywhere there are roads. There is no water. You will be about 20 minutes from the trail. .

NEXT BEST OPTION
You can camp down at the Lake at the Auxiliary Dam. This would be the first left off 178 just past the town of Lake Isabella exit. They charge a fee now, but there is a toilet. There is no water. You will be about 10 minutes from the trail

DELUXE OPTION BUT FAR FROM TRAIL
You can camp at one of the campgrounds in Kernville which are next to the Kern River. You will be about 40 minutes from the trail.

For more info on camping, lodging, recreation
Kern River Valley, Lake Isabella Source - CANYON CONNECTION

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For Kennedy Meadows Summer Trail Appreciation Days

TROY MEADOW:
53 miles northeast of Kernville via Mtn. 99 and Sherman Pass Rd. (22S05), or 34 miles west of Hwy. 395 via Nine Mile Canyon Rd. (J41). Paved roads; 73 units including 10 suitable for RV's up to 20'; restrooms; piped well water; no trash collection. Elev. 7,800 feet. Open Jun. to Nov. Depending on snow pack-check before you go early or late in the season  $5 per night fee.

DISPERSED CAMPING AREAS - On the Kern Plateau you will find many dispersed camping areas free of charge which are great for visitors with self-contained units and large groups. These areas may not have facilities and require a campfire permit. Some of the more popular areas include Troy Meadow overflow, Fish Creek overflow, Bonita Meadow, South Fork of the Kern River around Kennedy Meadows and Big Meadow.

For more info on camping, lodging, recreation
Kern River Valley, Kern Plateau - CANYON CONNECTION