A range of technologies require the directed motion of nanoscale droplets on solid substrates. A way of realizing this effect is durotaxis, whereby a stiffness gradient of a substrate can induce directional motion without requiring an energy source. Here, we report on the results of extensive molecular dynamics investigations of droplets on a surface with varying stiffness. We find that durotaxis is enhanced by increasing the stiffness gradient and, also, by increased wettability of the substrate, in particular, when droplet size decreases. We anticipate that our study will provide further insights into the mechanisms of nanoscale directional motion.