Will insulating attached garage walls create a moisture problem?
Chicago - Cold. Vapor barrier to inside. Moisture concern solved.
Half-concrete wall - if you only insulate the frame part, the concrete  part will still be wicked cold. You might want to consider insulating the frame part and then covering the whole wall (concrete part and stud bays) with rigid foam sheets, taped or sealed as the vapor barrier, and then drywall - which would give you some insulation over the concrete part.