Recommended! Die Fabrik Hostel, it is right in the heart of the Kreuzberg district (and, to be honest, where real Berliner life continues away from the hellish maw of global tourism!)
Those looking for a hotel-style accommodation with hostel prices, this is the one. Been going there since 1998 and makes part of why Berlin is so special to me! Has nice big rooms and cosy art deco style. So good, even real Germans stay there. Also has very nice and comfortable cafe adjoining it.
At Schlesische Str. 18, Kreuzberg. Nearest U-Bahn Schlesiche Tor
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