You can check out travelocity.com or priceline.com, and also some of the big US hotel chains: Best Western, Hampton Inn, Comfort Inn, etc.
If you're looking to save money (and frankly a quid won't get you nearly as far in the US as it would've a year ago) check out Hostelworld.com or Hostelbookers.com: their ratings are customer generated and tend to be pretty accurate.
LA has a mild climate and is reasonably pleasant year round (note that you can easily look up temperature forecasts online.) Frankly if you're going to go through all the trouble of getting out to LA I'd recommend seeing some other parts of California as well-- San Francisco, Yosemitie, driving along the coast in between LA and SF, and San Diego are all things I would put on my tourist list ahead of LA proper, which is really just a gigantic suburb. If you can squeeze in the grand canyon (roughly a day's drive from LA) I highly recommend that as well.
Also if you can't drive or are under 21 you might consider going with a package tour--you basically need a car to get around LA by yourself.