Cortical circuits are characterized by a high degree of structural and dynamical complexity, and this biological reality is reflected in the large number of parameters in even highly idealized cortical models. A fundamental task of computational neuroscience is to understand how these parameters govern network dynamics. While some neuronal parameters can be measured in vivo , many remain poorly constrained due to limitations of available experimental techniques. Computational models can address this problem by relating difficult-to-measure parameters to observable quantities, but to do so one must overcome two challenges: (1) the computational expense of mapping a high dimensional parameter space, and (2) extracting biological insights from such a map. This study aims to address these challenges in the following ways: First, we propose a data-informed, parsimonious mean-field algorithm that efficiently predicts spontaneous cortical activity, thereby speeding up the mapping of parameter landscapes. Second, we show that lateral inhibition provides a basis for conceptualizing cortical parameter space, enabling us to begin to make sense of its geometric structure and attendant scaling relations. We illustrate our approach on a biologically realistic model of the Macaque primary visual cortex.