Many self-configuration problems that occur in sensor networks, such as clustering or operator placement for in-network data aggregation, can be modeled as facility location problems. Unfortunately, existing distributed facility location algorithms are hardly applicable to multi-hop sensor networks. Based on an existing centralized algorithm, we therefore devise equivalent distributed versions which, to our knowledge, represent the first distributed approximations of the facility location problem that can be practicably implemented in multi-hop sensor networks with local communication. Through simulation studies, we demonstrate that, for typical instances derived from sensor-network configuration problems, the algorithms terminate in only few communication rounds, the runtime does not increase with the network size, and, finally, that our implementation requires only local communication confined to small network neighborhoods. In addition, we propose simple extensions to our algorithms to support dynamic networks with varying link qualities and node additions and deletions. Using link quality traces collected from a real sensor network deployment, we demonstrate the effectiveness of our algorithms in realistic multi-hop sensor networks.