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I work remote from central Los Angeles. The biking is incredible here. I mainly do hills and the Santa Monica/San Gabriel mountains provide some excellent climbing. There is very little traffic in the hilly parts of the city.
From central/Downtown LA, you can take Venice all the way to the beach with a dedicated bike lane. I rarely go on trails, as I only have a road bike. My favorite trip is to take the bus to somewhere north of Malibu and ride along the PCH for about 20 miles. Off-topic, but LA really does have great public transportation. It covers nearly the entire metro area such that you can get pretty much anywhere and only have to…
I like Ventura Blvd in the Valley to make it to the beach. It is congested at points earlier on (east), but then it clears out. Venice is busy almost the entire stretch.