Go to ocatv.com for show tickets. there are a bunch on there. i have been to the american idol finale 2 years in a row!
Otherwise, go to hollywood, check out the walk of fame, and definitely Venice beach on the weekend to see the freak show there. In-n-out burger is a must when coming out here... they are everywhere. i know you said no to theme parks, but universal studios and citywalk is awesome for teens. good luck, and have fun!
Try the out of the way places--look at the events page in the LA Times online, second section, for ideas. The city is sprawling and frenetic, and nice to visit this time of the year.
Huntington Beach (Surf City) is a nice diversion for anyone and not that far away.