It takes place in all parts of the plant. Just as it takes place in all living cells in all living organisms, Don't confuse respiration in plants with photosynthesis.
Actually, the term is transpiration... animals perform respiration... plants transpire through stomata... cellular structures on the surface of their leaves... at least vascular plants, i.e., those above mosses and algaes...
Plants do indeed perform respiration and, as drestie quite rightly pointed out, it occurs in the mitochondria (which are organelles situated in almost all palnts cells.)
Of course, both shammydodger and drestie are correct. My emphasis was on a different understanding of the question's intent. Living plant cells survive the night-time and cloudy days by respiration,(but does take place at other times as well) most of which takes place in the cell's mitochondria... my focus was on the dual purpose of transpiration...refrigerating the plant and carrying, towards the leaves, the nutrients coming from the roots... Thanx for straightening that out!