Phrase meaning "North, but not directly North, from here"
Perhaps
The prize is somewhere
to the north
That sounds less due north-ish than “north from here”. Otherwise, just replacing ‘from’ with ‘of’ would make it less specific too. ‘Somewhere north of here’ does not to me imply going straight up north—I’d place Toronto as ‘somewhere north of’ New York, for example.
Edit:
An even simpler solution just occurred to me:
The prize is
further north
I would say The prize is further North than here.