Associating geo-coordinates with the content of social media posts can enhance many existing applications and services and enable a host of new ones. Unfortunately, a majority of social media posts are not tagged with geo-coordinates. Even when location data is available, it may be inaccurate, very broad or sometimes fictitious. Contemporary location estimation approaches based on analyzing the content of these posts can identify only broad areas such as a city, which limits their usefulness. To address these shortcomings, this paper proposes a methodology to narrowly estimate the geo-coordinates of social media posts with high accuracy. The methodology relies solely on the content of these posts and prior knowledge of the wide geographical region from where the posts originate. An ensemble of language models, which are smoothed over non-overlapping sub-regions of a wider region, lie at the heart of the methodology. Experimental evaluation using a corpus of over half a million tweets from New York City shows that the approach, on an average, estimates locations of tweets to within just 2.15km of their actual positions.