The advent of 5G technology has opened up new opportunities across various fields, including healthcare. In the context of wireless communication, the deployment of a two-tier heterogeneous network (HetNet) plays a crucial role in ensuring robust connections among devices, users, and healthcare infrastructure. This study focuses on optimizing coverage and energy efficiency (EE) in HetNets, tailored for specific application domains. We begin by examining how antenna height impacts coverage within macro and pico cells. Precise antenna placement is critical, as it significantly alters coverage patterns, particularly in healthcare settings, which can range from large hospital complexes to remote telemedicine locations. Additionally, we investigate the strategic adjustment of antenna gain in macro and pico cells, showing how this optimization enhances coverage and minimizes interference. Achieving this balance is essential for the reliable transmission of data. Our research also considers the interplay of antenna height, EE, and the maximum number of users ($N_{max}$). Surprisingly, we find that $N_{max}$ has a limited impact on coverage and EE compared to antenna configuration. This emphasizes the crucial role of antenna design and placement in crafting efficient wireless networks.Our study provides insights into improving coverage and EE in HetNets, with implications for various applications. It underscores the importance of strategic antenna optimization in shaping efficient and resilient communication systems. Furthermore, we explore the impact of $\beta$ on EE and leverage idle mode capabilities for further EE enhancements.