Modern society habitually uses online social media services to publicly share observations, thoughts, opinions, and beliefs at any time and from any location. These geotagged social media posts may provide aggregate insights into people's perceptions on a bad range of topics across a given geographical area beyond what is currently possible through services such as Yelp and Foursquare. This paper develops probabilistic language models to investigate whether collective, topic-based perceptions within a geographical area can be extracted from the content of geotagged Twitter posts. The capability of the methodology is illustrated using tweets from three areas of different sizes. An application of the approach to support power grid restoration following a storm is presented.