Don't stare at the ground — look at me.

Literal

Eyes [obj-を] ground [to-に] dropping [negative-ていないで], me [obj-を] look [imperative-なさい].

目を落とす ('drop one's eyes') means 'cast one's gaze downward.' ~ていないで is the negative progressive te-form meaning 'stop doing X and...' — it connects the negated ongoing action to the positive command that follows.