When I had to stay overnight in LAX for an early morning flight I stayed at this place: https://wr.wyndhamrewards.com/hotels...n_date&rooms=1

It's nothing special at all, but it's cheap, has a shuttle, and is pretty clean. I wouldn't wander too far away, though - I have a Losangelephobia, but even still it didn't seem to be the best area. But if you stay in the hotel or the Arby's next door, they should be good.