The Autrey National Center is located directly across the street from the Los Angeles Zoo. It's actually a very nice little center with the Museum of the American West, the Wells Fargo theater, museum gift shop and a cafe. It cost $9 for an adult with free parking.
On display at the museum is art, artifacts, old clothing, and lots of clothes, guns and other items used in famous television shows and movies. On display and not pictured here are the costumes from shows like Gunsmoke and The Lone Ranger, and ornate costumes of country western stars and singers.
On the weekend you can even experience panning for gold it the quaint little courtyard made to look like a small mining area complete with waterfall. If you're wondering what to do for the day and don't want to spend a huge chunk of money, this might definitely be worth a trip for you.