Well, after reading this thread, I must admit that FTers are very resourceful about getting around S. Cal without a car.
But, I've been to most of the shopping spots mentioned and I wouldn't try it without a car. Takes waaay too long and way too inconvenient.
The idea about staying near the Beverly Center is a good one--and I would add that The Grove Center which is really nicer is nearby.
http://www.thegrovela.com/ Also, the Grove is right next door to the old-time Farmer's Market (not really a farmer's market, but an old and funky shopping and restaurant area--try the Beignets and Cafe au Lait at the Gumbo Pot).
DO NOT take public transport to the Citadel Outlet. The area is not good. Okay if you drive into the Center.