Currently, most of the processing techniques for the conventional location-based queries focus only on a single type of objects. However, in real-life applications the user may be interested in obtaining information about different types of objects, in terms of their neighboring relationship. We term the different types of objects closer to each other the heterogeneous neighboring objects (HNOs for short). Efficient processing of the location-based queries on the HNOs is more complicated than that on a single data source, because the neighboring relationship between the HNOs inevitably affects the query result. In this paper, we present a novel and important query on the HNOs, namely the shortest average-distance query (SAvgDQ for short), which can provide useful object information by considering both the spatial closeness of objects to the query object and the neighboring relationship between objects. Given a query object q and a distance d, the SAvgDQ retrieves a set of HNOs, such that the distances between any two objects in this set are less than or equal to d and its average distance to q is the smallest among all HNOs sets. To efficiently process the SAvgDQ, we develop an algorithm, the SAvgDQ processing algorithm, which operates based on three devised heuristics, the HNOs-qualifying heuristic, the HNOs-pruning heuristic, and the SAvgD-pruning heuristic, to reduce the number of distance computations required for query processing. Comprehensive experiments are conducted to demonstrate the effectiveness of the heuristics and the efficiency of the proposed algorithm.