Unlike other cities there are different areas to check out that are miles and miles apart...and each one has its pros and cons.
Beverly Hills, Santa Monica, Downtown, Manhattan Beach, Pasadena, Hollywood, Orange County (Disneyland, South Coast)
-As a fan of both, and because they're going to be playing in October, I'd DEFINITELY check out a USC football game and Dodgers playoff game. If you're a sports fan and the schedule allows it, you should most definitely check it out
-Each section of the city previously mentioned has their fair share of touristy places, cool places, good restaurants/bars/hangouts.
-I would +1,000 the Getty. That, for sure, should be part of your visit. I also hear the newly renovated Griffith Observatory is a good hangout spot.
-B. Hills/Rodeo Drive is a very cool area to check out for shopping dining and you have a realllllly good chance of spotting a celebrity.
Regardless of what you decide, I would use the LA Magazine as a good guide for dining/drinking/shopping....they do a good job of breaking down LA IMO...
http://www.lamag.com/