I stayed at the Sogo Hotel for 6 nights while moving to LA. It's an old but well kept building in Little Tokyo that's clean and comfortable. There are a bunch of long-term residents so the place has a friendly dorm kind of atmosphere, but it's nice and quiet at the same time.
The building is right near a metro stop and the center of Little Tokyo, so it's very convenient too. The area feels pretty safe and it's quiet at night.
The price makes it one of the best deals in central LA, and I'd definitely stay there again.