Fluorescent molecular rotors (FMRs) belong to an important class of environment-sensitive dyes capable of acting as nanoprobes in the measurement of viscosity and polarity of their micro-environment. FMRs have found widespread applications in various research fields, ranging from analytical to biochemical sciences, for example in intracellular imaging studies or in volatile organic compound detection. Here, a computational investigation of a recently proposed FMR, namely 4-(diphenylamino)phthalonitrile (DPAP), in various chemical environments is presented. A purposely developed molecular mechanics force field is proposed and then applied to simulate the rotor in a high- and low-polar solvent (i.e., acetonitrile, tetrahydrofuran, o-xylene and cyclohexane), a polymer matrix and a lipid membrane. Subtle effects of the molecular interactions with the embedding medium, the structural fluctuations of the rotor and its rotational dynamics are analyzed in some detail. The results correlate with a previous work, thus supporting the reliability of the model, and provide further insights into the environment-specific properties of the dye. In particular, it is shown how molecular diffusion and rotational correlation times of the FMR are affected by the surrounding medium and how the molecular orientation of the dye becomes anisotropic once immersed in the lipid bilayer. Moreover, a qualitative correlation between the FMR rotational dynamics and the fluorescence lifetime is detected, a result in line with the observed viscosity dependence of its emission. Finally, optical absorption spectra are computed and successfully compared with their experimental counterparts.