In several migratory cells, the microtubule-organizing center (MTOC) is repositioned between the leading edge and nucleus, creating a polarized morphology. Although our understanding of polarization has progressed as a result of various scratch-wound and cell migration studies, variations in culture conditions required for such assays have prevented a unified understanding of the intricacies of MTOC and nucleus positioning that result in cell polarization. Here, we employ a new SMRT (for sparse, monolayer, round, triangular) analysis that uses a universal coordinate system based on cell centroid to examine the pathways regulating MTOC and nuclear positions in cells plated in a variety of conditions. We find that MTOC and nucleus positioning are crucially and independently affected by cell shape and confluence; MTOC off-centering correlates with the polarization of single cells; acto-myosin contractility and microtubule dynamics are required for single-cell polarization; and end binding protein 1 and light intermediate chain 1, but not Par3 and light intermediate chain 2, are required for single-cell polarization and directional cell motility. Using various cellular geometries and conditions, we implement a systematic and reproducible approach to identify regulators of MTOC and nucleus positioning that depend on extracellular guidance cues.