What about
http://www.meininger-hotels.com/

The central station hotel/hostel. My mother in law used it, and she didn't complain about it. You just have basic service, but it is clean and central. It seems, that the other hotels from this chain are also centrally located (except the airport (BBI) hotel). But I've never been in them.
cheers
757DUD

PS: For Berlin, just try to stay within the S-Bahn-Ring. From there you can reach most areas pretty convenient.