Unmanned aerial vehicle (UAV) has revealed its great advantage to provide efficient data collection and wireless charging services to wireless-power sensor networks (WPSNs). Note that the UAV usually is equipped with limited battery power and therefore may not have enough energy to visit all sensor nodes (SNs) during a flight. However, the energy consumption of the UAV is rarely discussed in UAV-assisted WPSNs. In this paper, we study visiting planning problem in the UAV-assisted WPSN by considering both the energy limitation of the UAV and the age of information (AoI) of data collection. Specifically, we introduce a mixed data collection strategy to reduce the AoI of the collected data and improve the energy efficiency of the UAV during each flight. The formulated AoI-aware problem, which aims to minimize the average AoI of the collected data and meanwhile maximize the number of visiting SNs as well as the amount of data, is further tackled by utilizing the reformulation-linearization-technique (RLT) and alternating direction method of multipliers (ADMM). The results show the proposed ADMM-based algorithm can outperform other approaches in terms of system objective and energy efficiency.