We perform computational investigations of the electrolyte-mediated interactions of charged nanoparticles with the walls of nanochannels. We investigate the role of discrete ion effects, valence, and electrolyte strength on nanoparticle-wall interactions. We find for some of the multivalent charge regimes that the like-charged nanoparticles and walls can have attractive interactions. We study in detail these interactions and the free-energy profile for the nanoparticle-wall separation. We find there are energy barriers and energy minima giving preferred nanoparticle locations in the channel near the center and at a distance near to but separated from the channel walls. We characterize contributions from surface overcharging, condensed layers, and overlap of ion double layers. We perform our investigations using coarse-grained particle-level simulations with Brownian dynamics, classical density functional theory, and the mean-field Poisson-Boltzmann theory. We discuss the implications of our results for phenomena in nanoscale devices.