The biggest one I am familiar with is in Baldwin Park. -Broken Horn Saddlery
When I lived in Southern California, this store was three floors of "stuff" and you might not see everything in one day. I don't know how big it is now.
Back then, their parking lot was way too small for the size store they had and it wasn't uncommon to drive around waiting for a spot or park somewhere else and walk
At that time they did cater to the western rider but I remember seeing plenty of English tack as well.
I left SoCal in 2003; I'm sure there are other tack stores, I don't know about; hopefully someone will come in and post.
I will say the prices at the Broken Horn store were very reasonable. The closer one gets to downtown LA the more expensive things get
Enjoy your visit!