Global network dynamics over distributed brain areas emerge from the local dynamics of each brain area. Conversely, global dynamics constrain local activity such that the whole system becomes self-organizing. The implicit coupling between local and global scales induces a form of circular causality that is characteristic of complex, coupled systems that show self-organization, such as the brain. Here we present a network model based on spiking neurons at the local level and large-scale anatomic connectivity matrices at the global level. We demonstrate that this multiscale network displays endogenous or autonomous dynamics of the sort observed in resting-state studies. Our special focus here is on the genesis of itinerant (wandering) dynamics and the role of multistable attractors, which are involved in the generation of empirically known functional connectivity patterns, if the global coupling causes the dynamics to operate in the critical regime. Our results provide once again support for the hypothesis that endogenous brain activity is critical.