Socially important locations are places which are frequently visited by social media users in their social media lifetime. Discovering socially important locations provides valuable information, such as which locations are frequently visited by a social media user, which locations are common for a social media user group, and which locations are socially important for a group of urban area residents. However, discovering socially important locations is challenging due to huge volume, velocity, and variety of social media datasets, inefficiency of current interest measures and algorithms on social media big datasets, and the need of massive spatial and temporal calculations for spatial social media analyses. In contrast, cloud computing provides infrastructure and platforms to scale compute-intensive jobs. In the literature, limited number of studies related to socially important locations discovery takes into account cloud computing systetns to scale increasing dataset size and to handle massive calculations. This study proposes a cloud-based socially important locations discovery algorithm of Cloud SS-ILM to handle volume and variety of social media big datasets. In particular, in this study, we used Apache Hadoop framework and Hadoop MapReduce programming model to scale dataset size and handle massive spatial and temporal calculations. The performance evaluation of the proposed algorithm is conducted on a cloud computing environment using Turkey Twitter social media big dataset. The experimental results show that using cloud computing systems for socially important locations discovery provide much faster discovery of results than classical algorithms. Moreover, the results show that it is necessary to use cloud computing systems for analyzing social media big datasets that could not be handled with traditional stand-alone computer systems. The proposed Cloud SS-ILM algorithm could be applied on many application areas, such as targeted advertisement of businesses, social media utilization of cities for city planners and local governments, and handling emergency situations.