Venue recommendation aims to assist users by making personalised suggestions of venues to visit, building upon data available from location-based social networks (LBSNs) such as Foursquare. A particular challenge for this task is context-aware venue recommendation (CAVR), which additionally takes the surrounding context of the user (e.g. the user's location and the time of day) into account in order to provide more relevant venue suggestions. To address the challenges of CAVR, we describe two approaches that exploit word embedding techniques to infer the vector-space representations of venues, users' existing preferences, and users' contextual preferences. Our evaluation upon the test collection of the TREC 2015 Contextual Suggestion track demonstrates that we can significantly enhance the effectiveness of a state-of-the-art venue recommendation approach, as well as produce context-aware recommendations that are at least as effective as the top TREC 2015 systems.