Charging many electric vehicles (EVs) might cause violations of cable ampacities, statutory voltage limits, and substation transformer ratings in power distribution grids. Besides affecting mobility patterns, autonomous driving will open new perspectives in terms of interactions with the power grid. This paper explores the potential of autonomous EVs of reducing grid congestions thanks to the possibility of reaching the most suitable recharging locations autonomously. We first develop an algorithm for the coordinated charging of non-autonomous EVs accounting for grid constraints. We then augment its formulation by modeling the charging locations as decision variables of the problem, adopting an efficient linear mixed-integer program based on a linearized grid model and McCormick (exact) relaxations to handle some bi-linear terms appearing in the formulation. Considering the CIGRE' benchmark system for LV residential grids, we compare non-autonomous versus autonomous EVs and show that the additional degree of freedom coming from autonomous driving achieves reducing grid congestions.