I must admit the Burbank Mall is pretty cool.
If you go to downtown LA, the jewelry district is cool to hang out in. McCarthur Park I actually liked, it's wide open and a good place to relax in the day, no stress.
I'm definitely into LA's energy. Plus consider you leave the somewhat scruffy downtown area and you're basically at the UCLA campus. It's nothing but expensive white houses there. Walk a few miles down Wilshire and hang a right on San Vicente, and you're at the Beverly Center. A great mall.
I like that you can go in one district that's shitty and then end up in a neighborhood with million-dollar properties.