I grew up in LA and still go back to visit pretty frequently. I don't think I could live there but I get why so many people live there...It is pretty damn nice in the winter time. The weather was a breezy 75 degrees and not a cloud in the sky the whole week I was there.
Feeling deficient in museums since I live in the mountains, I filled up museum culture (both science and art) by visiting the Los Angeles Natural History Museum and the LA County Museum of Art. I recommend both, though watch out at the NHM-during the week you are going to have to throw some serious elbows with school children on field trips if you want to get a good look at the mammal dioramas. The weekend is probably more mellow.
Dioramas at the Museum of Natural History