Actually, two organelles transport protein in a eukaryotic cell (multicellular organisms): (rough) Endoplasmic Recticulum and Golgi Apparatus.
The (rough) endoplasmic recticulum transport the newly synthesized proteins to the golgi apparatus from where they are transported to the various regions of the cell or outside the cell. Smooth endoplasmic recticulum is not associated with protein transport.
Proteins, carrying a signaling sequence, are transported from the endoplasmic recticulum, packaged into vesicles, to the golgi apparatus (or golgi complex or golgi bodies). These proteins are modified by enzymatic reactions as they move through the golgi apparatus. After processing, these proteins are either excreted from the cell or are sent to various locations within the cell.
It is difficult to pinpoint the location of these organelles within the cell as locations are different for mammals, plants, yeasts, etc. Generally, the golgi apparatus is found adjacent to the endoplasmic recticulum, which in turn is found throughout the cell but has a higher density near the nucleus.