Even though I grew up in LA, my first encounter with the Hollywood Bowl was Wakko burping the Blue Danube (watch video here). It's a 17,000 person capacity outdoor portal to some of the world's greatest performances. And it's tucked away in the Hollywood Hills. And it's BYOB. On nights when the LA Phil plays, you can go to the Bowl in the afternoon (if you can stand the heat) and watch them rehearse for free. Parking's a pain, but they've arranged super easy public transportation options. Last night, Philip Glass performed the score to Koyaanisqatsi while they played the film. It was really quite neat.
For more about the Hollywood Bowl check here: http://www.hollywoodbowl.com/