Gaints? Other than the mammoth spot west of Whiterun.

And..

Where can I mine Soul Gems, that does not require I first do the dark brotherhood quest?

mine soul gems in dwarven ruins and giants are all over the tundra areas in the middle of the map.

Any one mine better than the other?

Soul gems can be found easily in some Dungeons and high level enimies.Giants and Mammoths can literraly be found everywhere.But they are more common in the Tundra.