Fog Computing is a new paradigm that has been proposed by CISCO to take full advantage of the ever growing computational capacity of the near-user or edge devices (e.g., wireless gateways and sensors). The paradigm proposes an architecture that enables the devices to host functionality of various user-centric services. While the prospects of Fog Computing promise numerous advantages, development of Fog Services remains under-investigated. This article considers an opportunity of Fog implementation for Alert Services on top of Wireless Sensor Network (WSN) technology. In particular, we focus on targeted WSN-alert delivery based on spontaneous interaction between a WSN and hand-held devices of its users. For the alert delivery, we propose a Gravity Routing concept that prioritizes the areas of high user-presence within the network. Based on the concept, we develop a routing protocol, namely the Gradient Gravity Routing (GGR) that combines targeted delivery and resilience to potential sensor-load heterogeneity within the network. The protocol has been compared against a set of state-of-the-art solutions via a series of simulations. The evaluation has shown the ability of GGR to match the performance of the compared solutions in terms of alert delivery ratio, while minimizing the overall energy consumption of the network