The Menshutkin reaction represents the alkylation of tertiary amines by alkyl halide where the reactants are neutral and the products, quaternary ammonium salts, are two ions with opposite signs. The most commonly used organic solvents in quaternization reactions are volatile organic solvents (VOSs), namely acetone, anhydrous benzene, dry dichloromethane (DCM), dimethylformamide (DMF) and acetonitrile (ACN). The purpose of this work was to examine eutectic solvents as a “greener” alternative to conventional solvents so that quaternization reactions take place in accordance with the principles of green chemistry. Herein, sixteen eutectic solvents were used as replacements for volatile organic ones in quaternization reactions of isonicotinamide with substituted phenacyl bromides. The reactions were carried out at 80 °C by three synthetic approaches: conventional (4–6 h), microwave (20 min) and ultrasound (3 h). Microwave-assisted organic reactions produced the highest yields, where in several reactions, the yield was almost quantitative. The most suitable eutectic solvents were based on choline chloride (ChCl) as the hydrogen bond acceptor (HBA) and glycerol, oxalic or levulinic acid as hydrogen bond donors (HBDs). The benefits of these three deep eutectic solvents (DESs) as a medium for quaternization reactions are the simplicity of their preparation for large-scale production, with inexpensive, available and nontoxic starting materials, as well as their biodegradability.