hanem is for "not A, but (instead) B" contexts - here, the first part is not a negative that you are mentioning only to discard it and mention the real thing. He does, after all, look there, and the going there is not an "instead" action. So hanem would not be appropriate here.

You're negating the action - he does not go there. He doesn't move at all. So nem needs to be in front of the verb stem, displacing the suffix.