Molecular dynamics calculations are carried out on pure, Al-substituted, and In-substituted LLZO. The calculations show that the tendency of Al to occupy the 24d sites in LLZO lithium ion conductors is hypothesized here to negatively impact ionic conductivity. The room-temperature ionic conductivity of In-LLZO, in which the In resides at the 48g sites, is predicted to be an order of magnitude higher than Al-LLZO. Consideration of the simple tetrahedral topology of the lithium ion conduction network suggests that the increased conductivity arises because the 48g site sits at a bridge in the lithium ion conduction network. An immobile ion residing in this location blocks fewer lithium conduction pathways than an ion, such as Al, that preferentially occupies the 24d site located at a node within the network. In addition, the electronic structure calculations presented here indicate no large difference in the stabilities of tetragonal and cubic phases for the aluminum-substituted and indium-substituted compounds. In both cases, the cubic phase is more stable than the tetragonal phase. This indicates that it should be possible to make a cubic In-LLZO phase with significant conductivity enhancement over the cubic Al-LLZO phase.