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Recommending Points-of-Interest (POIs) is surfacing in many location-based applications. The literature contains personalized and socialized POI recommendation approaches which employ historical check-ins and social links to make recommendations. However these systems still lack customizability (incorporating session-based user interactions with the system) and contextuality (incorporating the situational context of the user), particularly in cold start situations, where nearly no user information is available. In this paper, we propose LikeMind, a POI recommendation system which tackles the challenges of cold start, customizability, contextuality, and explainability by exploiting look-alike groups mined in public POI datasets. LikeMind reformulates the problem of POI recommendation, as recommending explainable look-alike groups (and their POIs) which are in line with user's interests. LikeMind frames the task of POI recommendation as an exploratory process where users interact with the system by expressing their favorite POIs, and their interactions impact the way look-alike groups are selected out. Moreover, LikeMind employs "mindsets", which capture actual situation and intent of the user, and enforce the semantics of POI interestingness. In an extensive set of experiments, we show the quality of our approach in recommending relevant look-alike groups and their POIs, in terms of efficiency and effectiveness.