Two days is not enough for Los Angeles, so the only sensible plan is one that does not try. This one takes two halves of the city and does each properly.
Day one — the coast
Morning. Santa Monica pier early, Palisades Park along the cliff, coffee on Montana Avenue.
Midday. North on the PCH. Getty Villa if you booked it, El Matador if you did not. Lunch in Malibu.
Afternoon. Back via Venice — Abbot Kinney and the canals.
Evening. Dinner on Main Street, sunset from the beach.
Day two — the city
Morning. Downtown: Grand Central Market, the Bradbury, the Broad.
Midday. Up to Griffith Park. The Observatory, and the Hollywood sign view from the lawn.
Afternoon. Beverly Hills — Rodeo briefly, Greystone properly.
Evening. Hollywood for dinner and whatever is on at the Bowl, the Fonda or the Pantages.
The thing that makes it work
Those two days contain roughly ninety miles of driving and about eleven separate parking problems. An hourly chauffeur across each day turns a logistics exercise back into a holiday.