In short, lots. Depending on your particular teenager's interests, here are a few ideas to get the gray matter going: seeing the sights in Hollywood; cruising around Beverly Hills; shopping (OK, maybe window shopping) on Rodeo Drive; theme-park fun at places like Knott's Berry Farm and Six Flags Magic Mountain; hitting the sand at Venice Beach or Santa Monica; movie-themed action at places including Universal Studios or studio tours of the NBC or Sony Pictures lots; sporting events including LA Lakers (basketball), LA Dodgers (baseball), or LA Galaxy (soccer) games; and, finally, lots of outdoor action, including a day trip to Joshua Tree National Park (great rock-climbing) or a hike in the sprawling, and surprisingly accessible, Santa Monica Mountains National Recreation Area.