As part of the Swift/Ultraviolet-Optical Telescope Stars Survey, we present near-ultraviolet (NUV; 3000-1700 {AA}) point-source photometry for 103 Galactic open clusters. These data, taken over the span of the mission, provide a unique and unprecedented set of NUV point-source photometry on simple stellar populations. After applying a membership analysis fueled mostly by Gaia DR2 (Cat. I/345) proper motions, we find that 49 of these 103 have clear precise color-magnitude diagrams (CMDs) amenable to investigation. We compare the CMDs to theoretical isochrones and find good agreement between the theoretical isochrones and the CMDs. The exceptions are the fainter parts of the main sequence and the red giant branch in the uvw2-uvw1 CMDs, which is most likely due to either the difficulty of correcting for the red leak in the uvw2 filter or limitations in our understanding of UV opacities for cool stars. For the most part, our derived cluster parameters - age, distance, and reddening - agree with the consensus literature, but we find a few clusters that warrant substantial revision from literature values, notably NGC 2304, NGC 2343, NGC 2360, NGC 2396, NGC 2428, NGC 2509, NGC 2533, NGC 2571, NGC 2818, Collinder 220, and NGC 6939. A number of these are clusters in the third Galactic quadrant, where previous studies may have mistaken the disk sequence for the cluster. However, the Gaia DR2 proper motions clearly favor a different sequence. A number of clusters also show white dwarf and blue straggler sequences. We confirm the presence of extended main-sequence turnoffs in NGC 2360 and NGC 2818 and show hints of them in a number of other clusters that may warrant future spectroscopic study. Most of the clusters in the study have low extinction, and the rest are well fit by a "Milky Way-like" extinction law. However, Collinder 220 hints at a possible "LMC-like" extinction law. We finally provide a comprehensive point-source catalog to the community as a tool for future investigation.