Hey yo my favorite shop in LA is Santa Monica Ski and Sports. It used to be Doc's Ski Haus so searching for it might be weird.
Its that store. Doc's is now a different store and I can't attest to their quality. SMSS is rad though the guys there do good work and they have Full Tilts if you are in to that (nowhere else in LA has FT to my knowledge). They actually only carry ski gear, no snowboard stuff.
Also Ski Net Sports in Studio City is a good shop with a really big selection of boots. They aren't even really a full shop they mostly only sell boots and a few pairs of skis. They are a bit more pricey generally. I've never asked what boot fitting costs there but they usually charge more than SMSS for sharpening and that sort of thing.