Since your goal is a "limited" tour of Yosemite or JT, may I make this suggestion? I think it would be a pretty cool trip for you.
Saturday:
Land Saturday morning at LAX. Not too much traffic on Saturday. Drive to Highway 395 and then go north to June Lake area. You will be driving along the eastern side of the Sierras. You will pass Mt Whitney and other scenic areas. You should make it in 6 hours or less, unless you get side tracked. If time permits, you could spend some time at Mono Lake. Or a great hike in the June Lake area is the Yost Trail to Fern Lake in the Ansel Adams Wilderness. Perfect High Sierra views and you can just imagine Adams taking a picture of this lake with the granite mountain background. The hike is 3.4 miles round trip. Could be a little snow on the ground. Trailhead is near Silver Lake (part of the June Lake loop). Camp at the Oh Ridge! campground. Always car camping sites available. If you bring food, use the bear boxes. Altitude is 7,000 feet so it can get a little chilly at night. Real close to the town of June Lake for food, etc. The town of June Lake is like Mammoth was 40 years ago.
Sunday:
Assuming Tioga pass is open. Drive Hwy 120 to Yosemite. It is about 100 miles each way. Takes about 2.5 hours each way. You will pass through Tuolumne Meadows and then down into the canyon. I think for a car tour this is the most dramatic route. You can spend time seeing the highlights in Yosemite and get back to June Lake before dark. Monday morning drive back to LA via HWY 395, and stop to visit anything that looked interesting as time permits.
