Autonomous inspection of large geographical areas is a central requirement for efficient hazard detection and disaster management in future cyber-physical systems such as smart cities. In this regard, exploiting unmanned aerial vehicle (UAV) swarms is a promising solution to inspect vast areas efficiently and with low cost. In fact, UAVs can easily fly and reach inspection points, record surveillance data, and send this information to a wireless base station (BS). Nonetheless, in many cases, such as operations at remote areas, the UAVs cannot be guided directly by the BS in real-time to find their path. Moreover, another key challenge of inspection by UAVs is the limited battery capacity. Thus, realizing the vision of autonomous inspection via UAVs requires energy-efficient path planning that takes into account the energy constraint of each individual UAV. In this paper, a novel path planning algorithm is proposed for performing energy-efficient inspection, under stringent energy availability constraints for each UAV. The developed framework takes into account all aspects of energy consumption for a UAV swarm during the inspection operations, including energy required for flying, hovering, and data transmission. It is shown that the proposed algorithm can address the path planning problem efficiently in polynomial time. Simulation results show that the proposed algorithm can yield substantial performance gains in terms of minimizing the overall inspection time and energy. Moreover, the results provide guidelines to determine parameters such as the number of required UAVs and amount of energy, while designing an autonomous inspection system.