With the advent of location-based social networks, users can tag their daily activities in different locations through check-ins. These check-in locations signify user preferences for various socio-spatial activities and can be used to build their profiles to improve the quality of services in some applications such as recommendation systems, advertising, and group formation. To support such applications, in this paper, we formulate a new problem of identifying top-k Socio-Spatial co-engaged Location Selection (SSLS) for users in a social graph, that selects the best set of k locations from a large number of location candidates relating to the user and her friends. The selected locations should be (i) spatially and socially relevant to the user and her friends, and (ii) diversified in both spatially and socially to maximize the coverage of friends in the spatial space. This problem has been proved as NP-hard. To address the challenging problem, we first develop a branch-and-bound based Exact solution by designing some pruning strategies based on the derived bounds on diversity. To make the solution scalable for large datasets, we also develop an approximate solution by deriving the relaxed bounds and advanced termination rules to filter out insignificant intermediate results. To further accelerate the efficiency, we present one fast exact approach and a meta-heuristic approximate approach by avoiding the repeated computation of diversity at the running time. Finally, we have performed extensive experiments to evaluate the performance of our proposed models and algorithms against the adapted existing methods using four real-world large datasets.