Wal-Mart!
...
Okay, but seriously. Hmm, LA, huh? Nice! I don't live there myself, but as far as I've seen, the major attraction in San Diego, at least, is often the beach. I'd bet LA wouldn't be all that much different. So if you can somehow get a job as a lifeguard or something, great! That might be hard, though, since I'd best almost every teen in LA would be looking for a job as a beach lifeguard. Other options near the beach might be selling various things at small stores. It doesn't just have to be food, either; you might be able to get a job selling T-shirts and what-not.
If you like sports, you might be able to pull off a job working in a sports stadium or otherwise working for a team. For instance, you could be one of those vendors who walks around (or, alternatively, stands in a booth) for the Los Angeles Dodgers. And if you really like baseball, you can catch some of the good action if you're walking through the stands. You could also work for the team in other ways, if they hired you. Maybe posting flyers, or taking calls about tickets, or something.
Well, anyway, that's what I can think of right now. Hope everything goes well in LA, and don't let that dog get too lonely at home!