We present a uniform mid-infrared imaging and photometric survey of 36 young, nearby, star-forming clusters and groups using Spitzer IRAC and MIPS. We have confidently identified and classified 2548 young stellar objects (YSOs) using recently established mid-infrared color-based methods. We have devised and applied a new algorithm for the isolation of local surface density enhancements from point source distributions, enabling us to extract the overdense cores of the observed star-forming regions for further analysis. We have compiled several basic structural measurements of these cluster cores from the data, such as mean surface densities of sources, cluster core radii, and aspect ratios, in order to characterize the ranges for these quantities. We find that a typical cluster core is 0.39 pc in radius, has 26 members with infrared excess in a ratio of Class II to Class I sources of 3.7, is embedded in a A_K = 0.8 mag cloud clump, and has a surface density of 60 pc^–2. We examine the nearest neighbor distances among the YSOs in several ways, demonstrating similarity in the spacings between Class II and Class I sources but large member clusters appear more dense than smaller clusters. We demonstrate that near-uniform source spacings in cluster cores are common, suggesting that simple Jeans fragmentation of parsec-scale cloud clumps may be the dominant process governing star formation in nearby clusters and groups. Finally, we compare our results to other similar surveys in the literature and discuss potential biases in the data to guide further interpretation.