During the last decades, the study of cities has been transformed by new approaches combining engineering and complexity sciences. Network theory is playing a central role, facilitating the quantitative analysis of crucial urban dynamics, such as mobility, city growth or urban planning. In this work, we focus on the spatial aspects of congestion. Analyzing a large amount of real city networks, we show that the location of the onset of congestion changes according to the considered urban area, defining, in turn, a set of congestion regimes separated by abrupt transitions. To help unveiling these spatial dependencies of congestion (in terms of network betweenness analysis), we introduce a family of planar road network models composed of a dense urban center connected to an arboreal periphery. These models, coined as GT and DT-MST models, allow us to analytically, numerically and experimentally describe how and why congestion emerges in particular geographical areas of monocentric cities and, subsequently, to describe the congestion regimes and the factors that promote the appearance of their abrupt transitions. We show that the fundamental ingredient behind the observed abrupt transitions is the spatial separation between the urban center and the periphery, and the number of separate areas that form the periphery. Elaborating on the implications of our results, we show that they may have an influence on the design and optimization of road networks regarding urban growth and the management of daily traffic dynamics.