Solubility is not only a crucial physicochemical property for laboratory practice but also provides valuable insight into the mechanism of saturated system organization, as a measure of the interplay between various intermolecular interactions. The importance of these data cannot be overstated, particularly when dealing with active pharmaceutical ingredients (APIs), such as dapsone. It is a commonly used anti-inflammatory and antimicrobial agent. However, its low solubility hampers its efficient applications. In this project, deep eutectic solvents (DESs) were used as solubilizing agents for dapsone as an alternative to traditional solvents. DESs were composed of choline chloride and one of six polyols. Additionally, water–DES mixtures were studied as a type of ternary solvents. The solubility of dapsone in these systems was determined spectrophotometrically. This study also analyzed the intermolecular interactions, not only in the studied eutectic systems, but also in a wide range of systems found in the literature, determined using the COSMO-RS framework. The intermolecular interactions were quantified as affinity values, which correspond to the Gibbs free energy of pair formation of dapsone molecules with constituents of regular solvents and choline chloride-based deep eutectic solvents. The patterns of solute–solute, solute–solvent, and solvent–solvent interactions that affect solubility were recognized using Orange data mining software (version 3.36.2). Finally, the computed affinity values were used to provide useful descriptors for machine learning purposes. The impact of intermolecular interactions on dapsone solubility in neat solvents, binary organic solvent mixtures, and deep eutectic solvents was analyzed and highlighted, underscoring the crucial role of dapsone self-association and providing valuable insights into complex solubility phenomena. Also the importance of solvent–solvent diversity was highlighted as a factor determining dapsone solubility. The Non-Linear Support Vector Regression (NuSVR) model, in conjunction with unique molecular descriptors, revealed exceptional predictive accuracy. Overall, this study underscores the potency of computed molecular characteristics and machine learning models in unraveling complex molecular interactions, thereby advancing our understanding of solubility phenomena within the scientific community.