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Fog computing is an emerging paradigm that aims to improve the efficiency and QoS of cloud computing by extending the cloud to the edge of the network. This paper develops a comprehensive energy efficiency analysis framework based on mathematical modeling and heuristics to study the offloading of virtual machine (VM) services from the cloud to the fog. The analysis addresses the impact of different factors including the traffic between the VM and its users, the VM workload, the workload versus number of users profile and the proximity of fog nodes to users. Overall, the power consumption can be reduced if the VM users traffic is high and/or the VMs have a linear power profile. In such a linear profile case, the creation of multiple VM replicas does not increase the computing power consumption significantly (there may be a slight increase due to idle / baseline power consumption) if the number of users remains constant, however the VM replicas can be brought closer to the end users, thus reducing the transport network power consumption. In our scenario, the optimum placement of VMs over a cloud-fog architecture significantly decreased the total power consumption by 56% and 64% under high user data rates compared to optimized distributed clouds placement and placement in the existing AT&T network cloud locations, respectively.