Gold nanoparticles of different shapes and sizes, including nanospheres, nanocubes, nanobranches, nanorods, and nanobipyramids, were dispersed into water-glycerol mixtures of varying volume ratios to investigate the response of their surface plasmon peaks to the refractive index of the surrounding medium. The refractive index sensitivities and figures of merit were found to be dependent on both the shape and the size of the An nanoparticles. The index sensitivities generally increase as An manoparticles become elongated and their apexes become sharper. An nanospheres exhibit the smallest refractive index sensitivity of 44 nm/RIU and Au nanobranches exhibit the largest index sensitivity of 703 nm/RIU. Au nanobipyramids possess the largest figures of merit, which increase from 1.7 to 4.5 as the aspect ratio is increased from 1.5 to 4.7.