I commute in and around downtown LA. I use the bike lanes and paths when I can, and the rest of the time I just ride way out in the middle of the right-hand lane. When the motorists honk, I know they can see me, so I pull over to let them pass when it's convenient.
(I have to admit I get a self-righteous thrill when the occasional aggressive/rude/egotistical driver leans on the horn and makes a jackass out of himself.)
Even the busiest parts of LA have quiet residential streets with little or no traffic. It's worth a few minutes of detour to keep my life and limbs a few years longer.