A series of 1,3,5-triazinyl aminobenzenesulfonamides substituted by aminoalcohol, aminostilbene, and aminochalcone structural motifs was synthesized as potential human carbonic anhydrase (hCA) inhibitors. The compounds were evaluated on their inhibition of tumor-associated hCA IX and hCA XII, hCA VII isoenzyme present in the brain, and physiologically important hCA I and hCA II. While the test compounds had only a negligible effect on physiologically important isoenzymes, many of the studied compounds significantly affected the hCA IX isoenzyme. Several compounds showed activity against hCA XII; (E)-4-{2-[(4-[(2,3-dihydroxypropyl)amino]-6-[(4-styrylphenyl)amino]-1,3,5-triazin-2-yl)amino]ethyl}benzenesulfonamide (31) and (E)-4-{2-[(4-[(4-hydroxyphenyl)amino]-6-[(4-styrylphenyl)amino]-1,3,5-triazin-2-yl)amino]ethyl}benzenesulfonamide (32) were the most effective inhibitors with KIs = 4.4 and 5.9 nM, respectively. In addition, the compounds were tested against vancomycin-resistant Enterococcus faecalis (VRE) isolates. (E)-4-[2-({4-[(4-cinnamoylphenyl)amino]-6-[(4-hydroxyphenyl)amino]-1,3,5-triazin-2-yl}amino)ethyl]benzenesulfonamide (21) (MIC = 26.33 µM) and derivative 32 (MIC range 13.80–55.20 µM) demonstrated the highest activity against all tested strains. The most active compounds were evaluated for their cytotoxicity against the Human Colorectal Tumor Cell Line (HCT116 p53 +/+). Only 4,4’-[(6-chloro-1,3,5-triazin-2,4-diyl)bis(iminomethylene)]dibenzenesulfonamide (7) and compound 32 demonstrated an IC50 of ca. 6.5 μM; otherwise, the other selected derivatives did not show toxicity at concentrations up to 50 µM. The molecular modeling and docking of active compounds into various hCA isoenzymes, including bacterial carbonic anhydrase, specifically α-CA present in VRE, was performed to try to outline a possible mechanism of selective anti-VRE activity.