Camouflaging data by generating fake information is a well-known obfuscation technique for protecting data privacy. In this paper, we focus on a very sensitive and increasingly exposed type of data: location data. There are two main scenarios in which fake traces are of extreme value to preserve location privacy: publishing datasets of location trajectories, and using location-based services. Despite advances in protecting (location) data privacy, there is no quantitative method to evaluate how realistic a synthetic trace is, and how much utility and privacy it provides in each scenario. Also, the lack of a methodology to generate privacy-preserving fake traces is evident. In this paper, we fill this gap and propose the first statistical metric and model to generate fake location traces such that both the utility of data and the privacy of users are preserved. We build upon the fact that, although geographically they visit distinct locations, people have strongly semantically similar mobility patterns, for example, their transition pattern across activities (e.g., working, driving, staying at home) is similar. We define a statistical metric and propose an algorithm that automatically discovers the hidden semantic similarities between locations from a bag of real location traces as seeds, without requiring any initial semantic annotations. We guarantee that fake traces are geographically dissimilar to their seeds, so they do not leak sensitive location information. We also protect contributors to seed traces against membership attacks. Interleaving fake traces with mobile users' traces is a prominent location privacy defense mechanism. We quantitatively show the effectiveness of our methodology in protecting against localization inference attacks while preserving utility of sharing/publishing traces.