Microstructured surfaces provide a unique framework to probe cell migration and cytoskeletal dynamics in a standardized manner. Here, we report on the steady-state occupancy probability of cells in asymmetric two-state microstructures that consist of two fibronectin-coated adhesion sites connected by a thin guidance cue. In these dumbbell-like structures, cells transition between the two sites in a repeated and stochastic manner, and average dwell times in the respective microenvironments are determined from the cell trajectories. We study the dynamics of human breast carcinoma cells (MDA-MB-231) in these microstructures as a function of area, shape, and orientation of the adhesion sites. On square adhesive sites with different areas, we find that the occupancy probability ratio is directly proportional to the ratio of corresponding adhesion site areas. These asymmetries are well captured by a simple model for the stochastic nonlinear dynamics of the cells, which reveals generic features of the motion. Sites of equal area but different shape lead to equal occupancy if shapes are isotropic (e.g., squared or circular). In contrast, an asymmetry in the occupancy is induced by anisotropic shapes like rhombi, triangles, or rectangles that enable motion in the direction perpendicular to the transition axis. Analysis of the two-dimensional motion of cells between two rectangles with orthogonal orientation suggests that cellular transition rates depend on the cell polarization induced by anisotropic micropatterns. Taken together, our results illustrate how two-state micropatterns provide a dynamic migration assay with distinct dwell times and relative cell occupancy as readouts, which may be useful to probe cell-microenvironment interactions.