The Spitzer Survey of Stellar Structure in Galaxies is a volume, magnitude, and size-limited survey of 2352 nearby galaxies with deep imaging at 3.6 and 4.5 mu m. In this paper, we describe our surface photometry pipeline and showcase the associated data products that we have released to the community. We also identify the physical mechanisms leading to different levels of central stellar mass concentration for galaxies with the same total stellar mass. Finally, we derive the local stellar mass-size relation at 3.6 mu m for galaxies of different morphologies. Our radial profiles reach stellar mass surface densities below similar to 1 M-circle dot pc(-2). Given the negligible impact of dust and the almost constant mass-to-light ratio at these wavelengths, these profiles constitute an accurate inventory of the radial distribution of stellar mass in nearby galaxies. From these profiles we have also derived global properties such as asymptotic magnitudes (and the corresponding stellar masses), isophotal sizes and shapes, and concentration indices. These and other data products from our various pipelines (science-ready mosaics, object masks, 2D image decompositions, and stellar mass maps) can be publicly accessed at IRSA (http://irsa.ipac.caltech.edu/data/SPITZER/S4G/).