This paper examines the location traces of 489 users of a location sharing social network for relationships between the users' mobility patterns and structural properties of their underlying social network. We introduce a novel set of location-based features for analyzing the social context of a geographic region, including location entropy, which measures the diversity of unique visitors of a location. Using these features, we provide a model for predicting friendship between two users by analyzing their location trails. Our model achieves significant gains over simpler models based only on direct properties of the co-location histories, such as the number of co-locations. We also show a positive relationship between the entropy of the locations the user visits and the number of social ties that user has in the network. We discuss how the offline mobility of users can have implications for both researchers and designers of online social networks.