The Southwest Museum is tucked away on a hillside in an older section of Los Angeles - Highland Park. It is a standard field trip destination for some of the local elementary schools, but it's great for an afternoon's stroll through the local history. They have an amazing collection of Native-American crafts, especially baskets. You'll see anything from huge baskets a grown person could hide in to something the size of an infant's hand. Some of the displays have seen better days, but they're still delightful to experience. The gift shop/bookstore has an interesting selection of items from local artists and writers. The museum staff are congenial and always willing to answer your questions.
Pros: basket collection, parking
Cons: hidden away