From LA take the 405 merging with the 5 and then take a right on the Antelope Valley Fwy (California Hwy 14) past Palmdale & Edwards Air Force Base to Mojave and Primo Burgers. Hwy 14 will turn into Hwy 395 as you go north. Pass through Red Rock Canyon and stop outside of Little Lake just before Red Hill Cinder Cone for a short walk to Fossil Falls. Overnight in Lone Pine to see the Alabama Hills and the Lone Pine Film Museum. Drive up the Eastern Sierra via Whitney Portal Road for a nice stop with a tiny trout pool and a very nice waterfall. Moving on toward Independence stop at Manzanar and the Mt Whitney Fish Hatchery. Bypass the road to the Ancient Bristlecone Pine Forest outside of Big Pine. Check out the Paiute Palace Casino outside of Bishop. Pass Lake Crowley and stop at the visitor's center at Mono Lake. Continue up Sherwin Grade and get a lunch in Bridgeport. Follow the West Walker River to the Nevada border.
Topaz Inn & Casino is just across the border. Finally leave 395 near Gardnerville to take Hwy 207 across the mountains into Stateline, Lake Tahoe. Travel west in South Lake Tahoe to the Taylor Creek Visitor Center for short walks and... there's an underground view through glass of the stream with fish. Continue west along the shore of Lake Tahoe to Emerald Bay and the vista point. Fallen Leaf Lake has it's own Fire Department and Post Office but it's a one-lane road to the south end of the lake. It's another beautiful drive along the east shore past Sand Harbor Beach. On the north shore there are the beautiful homes in Incline Village and the casinos at the state line west end of Crystal Bay.
On the return trip enter the June Lake Loop from the north to get the best view of what I call 'Little Yosemite Valley'. Grant Lake, Silver Lake and then a couple of beautiful waterfalls. Tiny Gull Lake and finally June Lake. Overnight in the town of Mammoth. Take Lake Mary Road to Lower Twin Lakes and Robinson Creek. Leave early to make it back to LA with 6 hours of driving time.