By integrating mesoscale models for hydrodynamics and micromechanics, we examine fluid-driven motion of vesicles on compliant surfaces. The vesicles, modeled as fluid-filled elastic shells, represent biological cells or polymeric microcapsules. Focusing on nonspecific interactions between these vesicles and synthetic substrates, we isolate mechanically and topographically patterned surfaces that transmit stop and go instructions, causing the vesicles to halt at specific locations, and with an increase in the flow velocity, to resume moving. For surfaces containing arrays of compliant posts, the substrates also affect the vesicles' gait, causing them to "crawl," "walk," or "jump." The latter behavior could promote the intermixing of reactants that are encapsulated within the microcapsules. Such control over vesicle dynamics can facilitate various biological assays and fabrication of arrays of mobile microreactors.