To many location-based service applications that prefer diverse results, finding locations that are spatially diverse and close in proximity to a query point (e.g., the current location of a user) can be more useful than finding the k nearest neighbors/locations. In this paper, we investigate the problem of searching for the k Diverse-Near Neighbors (kDNNs) in spatial space that is based upon the spatial diversity and proximity of candidate locations to the query point. While employing a conventional distance measure for proximity, we develop a new and intuitive diversity metric based upon the variance of the angles among the candidate locations with respect to the query point. Accordingly, we create a dynamic programming algorithm that finds the optimal kDNNs. Unfortunately, the dynamic programming algorithm, with a time complexity of O(kn3), incurs excessive computational cost. Therefore, we further propose two heuristic algorithms, namely, Distance-based Browsing (DistBrow) and Diversity-based Browsing (DivBrow) that provide high effectiveness while being efficient by exploring the search space prioritized upon the proximity to the query point and spatial diversity, respectively. Using real and synthetic datasets, we conduct a comprehensive performance evaluation. The results show that DistBrow and DivBrow have superior effectiveness compared to state-of-the-art algorithms while maintaining high efficiency. Copyright is held by the owner/author(s).