For a good cheap place to stay in LA the HI (YHA) in Santa Monica is a good bet. It's nice and cheap (though maybe a couple of dollars more than other hostels),clean & most importantly the hostel is safe and secure safe and secure. It's also only two minutes walk from Santa Monica Beach.
The kitchen is huge and always clean and tidy, the same goes for the eating area. The staff are curteous anf efficient - but a smile wouldn't have gone amiss.
Next door is a travel shop through which you can book bus tours to all the major attractions and they are pretty good value too.
There's not a great deal of atmosphere to the place but if you're on a budget and looking for a place to use as a base whilst you tour LA you can't go far wrong. Theme: HostelComparison: less expensive than average