A primary objective in many fMRI studies is localization of functional areas, regions of the brain exhibiting synchronous activity. Independent component analysis (ICA) applied to resting-state fMRI data is a principal tool used for this purpose. However, out-of-the-box ICA algorithms do not perform well on single-subject fMRI data. We recently proposed a single-subject ICA model employing empirical group priors, which produces much more accurate results than competing methods. Here, we extend that model to incorporate spatial priors on the subject effects, thus leveraging subject-specific information shared across neighboring locations. A key element of our approach is the use of cortical-surface fMRI data rather than traditional volumetric fMRI data, where complex spatial dependencies arise due to cortical folding and the presence of multiple tissue classes. In cortical-surface data, by contrast, the spatial dependence structure is greatly simplified, facilitating spatial modeling. We employ recent advances in spatial statistics and Bayesian computation to build a computationally efficient model that is compatible with the triangular mesh structure of cortical surface data.