As a resident of LA, I'll tell you to go to San Francisco.
There's not much to do here as a tourist, really. I never know where to take visiting family here. Hollywood is overrated. Disneyland, if you're into that. San Francisco is much cooler (I grew up near there, so I'm a little biased.) Basically what gempress said! SF is a LOT prettier. I love Fisherman's Wharf, Alcatraz, boat rides on the bay, the Ghiradelli chocolate factory (yum!), Chinatown, and just walking around the city is nice.
Actually San Fran usually has nicer weather in the winter than in the summer...less fog. Probably warmer in LA though.
I live in Santa Monica, so I'm biased again, LOL. It's nice by the Promenade and the Pier...there's outdoor ice skating through the end of January which is kinda fun. West Hollywood is nice, too, plenty to walk to, super dog friendly and better for bars/clubs than Santa Monica. Marina del Rey is neat, small though, but you can take a water taxi around. I think they also have boats to Catalina Island, which is supposed to be pretty. Venice Beach is...interesting.
I'd recommend San Diego over LA though. There's the zoo, Sea World, the gaslight district, and it's a prettier town, and the beaches are nicer.
Actually, that's a good point! Or from LA to Santa Barbara.
I second SailinAero's recs for: The Getty, Amoeba and Roscoes! We now also have a Chick Fil A which is apparently a huge deal.
Sorry this post is so wandering, I was trying to respond to a lot of thoughts...