We have combined scanning tunneling microscopy with inelastic electron tunneling spectroscopy (IETS) and density functional theory (DFT) to study a tetracyanoethylene monolayer on Ag(100). Images show that the molecules arrange in locally ordered patterns with three nonequivalent, but undeterminable, adsorption sites. While scanning tunneling spectroscopy only shows subtle variations of the local electronic structure at the three different positions, we find that vibrational modes are very sensitive to the local atomic environment. IETS detects sizable mode frequency shifts of the molecules located at the three topographically detected sites, which permits us to determine the molecular adsorption sites through identification with DFT calculations.