The truth is the grid of Altbau (pre-war) buildings is great to live in, especially if you don't share the flat and can utilise the "back" room as a bedroom. But pretty much most side streets (at least in the West) are super quiet -- thanks to speed bumps, narrow lanes, treeline and wide sidewalks.

EDIT: Also many points are in heavy-industry areas (like Westhafen) so being far away from the street doesn't change much.