Points of interest (PoI) data serves an important role as a foundation for a wide variety of location-based services. Such data is typically obtained from an authoritative source or from users through crowdsourcing. It can be costly to maintain an up-to-date authoritative source, and data obtained from users can vary greatly in coverage and quality. We are also witnessing a proliferation of both GPS-enabled mobile devices and geotagged content generated by users of such devices. This state of affairs motivates the paper's proposal of techniques for the automatic discovery of PoI data from geo-tagged microblog posts. Specifically, the paper proposes a new clustering technique that takes into account both the spatial and textual attributes of microblog posts to obtain clusters that represent PoIs. The technique expands clusters based on a proposed quality function that enables clusters of arbitrary shape and density. An empirical study with a large database of real geo-tagged microblog posts offers insight into the properties of the proposed techniques and suggests that they are effective at discovering real-world points of interest.