Quiet location: Try to avoid a busy thoroughfare in your house, and if you put the litter box in a laundry utility room, place it far enough away from appliances, so that the noise from washers and dryers do not stress the cat.
If space is a problem, consider using an inexpensive screen in the corner of a living room or bedroom.
A guest bathroom would be ideal, or the closet of a guest bedroom.
Private location: Cats like privacy when they eliminate, not because of modesty, but because of a primal fear of being ambushed by an enemy when their guard is down.