In this work, we examine the effect of microstructure on ion-migration-induced photoluminescence (PL) quenching in methylammonium lead iodide perovskite films. Thin films were fabricated by two methods: spin-coating, which results in randomly oriented perovskite grains, and zone-casting, which results in aligned grains. As an external bias is applied to these films, migration of ions causes a quenching of the PL signal in the vicinity of the anode. The evolution of this PL-quenched zone is less uniform in the spin-coated devices than in the zone-cast ones, suggesting that the relative orientation of the crystal grains plays a significant role in the migration of ions within polycrystalline perovskite. We simulate this effect via a simple Ising model of ionic motion across grains in the perovskite thin film. The results of this simulation align closely with the observed experimental results, further solidifying the correlation between crystal grain orientation and the rate of ionic transport.