In South Korea, Jeju Island has a role as a test bed for electric vehicles (EVs). All conventional cars on the island are supposed to be replaced with EVs by 2030. Accordingly, how to effectively set up EV charging stations (EVCSs) that can charge EVs is an urgent research issue. In this paper, we present a case study on planning the locations of EVCS for Jeju Island, South Korea. The objective is to determine where EVCSs to be installed so as to balance the load of EVCSs while satisfying demands. For a public service with EVCSs by some government or non-profit organization, load balancing between EVCS locations may be one of major measures to evaluate or publicize the associated service network. Nevertheless, this measure has not been receiving much attention in the related literature. Thus, we consider the measure as a constraint and an objective in a mixed integer programming model. The model also considers the maximum allowed distance that drivers would detour to recharge their EV instead of using the shortest path to their destination. To solve the problem effectively, we develop a heuristic algorithm. With the proposed heuristic algorithm, a variety of numerical analysis is conducted to identify effects of the maximum allowed detour distance and the tightness of budget for installing EVCSs. From the analysis, we discuss the effects and draw practical implications.