There is actually a really great webpage that would be perfect in helping you find
Cheap Los Angeles Hotels. I would look at that as it gives you good advice on ways to save yourself some money. A good tip i have noticed is that you may find more reasonable rates if you stay in a hotel at one of the airports. This might not be in the heart of the city but it will be really easy to travel from here as they have shuttle services which run all day, either by bus or by train.
If staying at an Airport hotel doesnt appeal to you the Figueroa Hotel sounds like it may suit you better. This Moroccan themed hotel is located down town but still offers excelent room rates. I hope this helped.