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We experimentally investigate the local refractive index sensitivity of plasmonic gold nanodisks by applying small polymer dots to selected disk sites by means of two-step lithography. Measured sensitivity profiles obtained from tracking the polymer-induced spectral shift of the plasmon modes are in excellent agreement with numerical simulation of both spectral sensitivity and the electric near field of the nanodisks. Based on the nanodisk sensitivity profile we tailor a sensitive and spatially uniform plasmonic sensor by capping the disk with a dielectric layer, thus restricting analyte access to the disk rim.