Point-of-Interest (POI) recommender systems provide personalized recommendations to users and help businesses attract potential customers. Despite their success, recent studies suggest that highly data-driven recommendations could be impacted by data biases, resulting in unfair outcomes for different stakeholders, mainly consumers (users) and providers (items). Most existing fairness-related research works in recommender systems treat user fairness and item fairness issues individually, disregarding that RS work in a two-sided marketplace. This paper studies the interplay between (i) the unfairness of active users, (ii) the unfairness of popular items, and (iii) the accuracy (personalization) of recommendation as three angles of our study triangle. We group users into advantaged and disadvantaged levels to measure user fairness based on their activity level. For item fairness, we divide items into short-head, mid-tail, and long-tail groups and study the exposure of these item groups into the top-k recommendation list of users. Experimental validation of eight different recommendation models commonly used for POI recommendation (e.g., contextual, CF) on two publicly available POI recommendation datasets, Gowalla and Yelp, indicate that most well-performing models suffer seriously from the unfairness of popularity bias (provider unfairness). Furthermore, our study shows that most recommendation models cannot satisfy both consumer and producer fairness, indicating a trade-off between these variables possibly due to natural biases in data. We choose the POI recommendation as our test scenario; however, the insights should be trivially extendable on other domains.