Introduction Methicillin resistance, inducible clindamycin resistance (ICR), biofilm production, and increased minimum inhibitory concentration (MIC) of vancomycin in Staphylococcus aureus are major causes of antibiotic treatment failure and increased morbidity and mortality. The surveillance of such isolates and the study of their antimicrobial pattern are essential in managing the infections caused by these isolates. This study aimed to determine methicillin resistance, biofilm production, and ICR in S. aureus isolates from a tertiary care hospital in Kathmandu, Nepal. Materials and methods A total of 217 S. aureus isolated from different samples were processed following standard laboratory procedures. Antibiotic susceptibility testing was performed by the Kirby–Bauer disk diffusion technique. Methicillin-resistant S. aureus (MRSA) were identified by the cefoxitin disk diffusion test, and biofilm producers were examined using the microtiter plate technique. D-test and E-test were performed to determine inducible clindamycin resistance and minimum inhibitory concentration of vancomycin, respectively. Results Among the 217 S. aureus isolates, 78.3% were multidrug-resistant (MDR), 47.0% were MRSA, 62.2% were biofilm producers, and 50.7% showed ICR. All MRSA isolates exhibited MIC levels of vancomycin within the susceptible range. Biofilm producers and MRSA isolates showed elevated antimicrobial resistance. MRSA was significantly associated with MDR. Biofilm-producing and multidrug-resistant MRSA isolates showed significantly higher MIC levels of vancomycin (p = 0.0013 and < 0.0001, respectively), while ICR was significantly higher in MDR (p = 0.0001) isolates. Conclusion High multidrug resistance, MRSA, and ICR in this study call for routine evaluation of antibiotic susceptibility patterns of S. aureus. Vancomycin can be used to treat serious staphylococcal infections. Clindamycin should be prescribed only after performing the D-test. Drugs like teicoplanin, chloramphenicol, doxycycline, amikacin, and levofloxacin can treat MRSA infections.