Unmanned Aerial Vehicles (UAVs) are poised to play a central role in revolutionizing future services offered by the envisioned smart cities, thanks to their agility, flexibility, and cost-efficiency. UAVs are being widely deployed in different verticals including surveillance, search and rescue missions, delivery of items, and as an infrastructure for aerial communications in future wireless networks. UAVs can be used to survey target locations, collect raw data from the ground (i.e., video streams), generate computing task(s) and offload it to the available servers for processing. In this work, we formulate a multi-objective optimization framework for both the network resource allocation and the UAV trajectory planning problem using Mixed Integer Linear Programming (MILP) optimization model. In consideration of the different stake holders that may exist in a Cloud-Fog environment, we minimize the sum of a weighted objective function, which allows network operators to tune the weights to emphasize/de-emphasize different cost functions such as the end-to-end network power consumption (EENPC), processing power consumption (PPC), UAVs total flight distance (UAVTFD), and UAVs total power consumption (UAVTPC). Our optimization models and results enable the optimum offloading decisions to be made under different constraints relating to EENPC, PPC, UAVTFD and UAVTPC which we explore in detail. For example, when the UAVs propulsion efficiency (UPE) is at its worst (10% considered), offloading via the macro base station is the best choice and a maximum power saving of 34% can be achieved. Extensive studies on the UAVs coverage path planning (CPP) and computation offloading have been conducted, but none has tackled the issue in a practical Cloud-Fog architecture in which access, metro and core layers are considered in the service offloading in a distributed architecture like the Cloud-Fog.