Nice car camping spot near Lone Pine?

Hey gang,

I'm heading down 395 from Tahoe, for a wedding in Ventura next month, and Lone Pine is an approximate midpoint. Wondering if any of you guys know of any nice quiet spots to camp off of 395 anywhere near approximately Lone Pine area? Probably just for a night or two, it's just me, the dog, and my high-clearance 4WD. Ideal camping for me is dense shaded forest, water source, no traffic noise, and none to very few other humans. A fun day hike (fun for me is maybe 8-12 miles round trip 3000ft cumulative elevation gain max) with lake/peak destination would be nice but certainly not required. I would be passing through Wednesday / Thursday if it makes a difference.

I usually seek out national forest (because I have a dog), then find a campground, then look for sketchy jeep roads near the campground that, with a little exploration, end up at sweet undesignated camping areas -- these tend to be the best camping!

Check out Onion Valley. You could hike up to Kearsarge Pass if so inclined!

Great suggestions guys! I will do extensive internet research and hopefully have a trip report by this time next month.

It's not the "dense shaded forest" you've asked for, but I can't recommend dispersed camping in the Alabama Hills enough. It is our favorite car camping spot along the 395 when heading up to the Eastern Sierra.
Waking up to views of the rocks with the Sierra peaks in the distance is like none other. And it's free.