Index coding for broadcast channels allows each receiver or client to retrieve its demanded message from its side information and the transmitted codeword. In general, a client may have to observe the entire codeword to decode its demanded message. However, downloading or querying the codeword symbols might involve costs at a client - such as network utilization costs and storage. Traditional index coding does not consider this client perspective, and as a result, for these codes the number of codeword symbols queried by a client per decoded message symbol, which we refer to as locality, could be large. In this paper we study a 'client aware' approach to index coding by viewing the problem as a trade-off between the achievable broadcast rate and locality, where the objective is to minimize the rate for a given value of locality and vice versa. We first consider the minimum possible locality 1 and show that the coding scheme based on fractional coloring of the interference graph is optimal for this locality. We then propose index coding schemes with small locality by covering the side information graph using acyclic subgraphs and subgraphs of small minrank. We also show how locality can be accounted for in conventional partition multicast and cycle covering solutions to index coding, thereby yielding locally decodable index codes. © 2018 IEEE.