In recent years, a plethora of solutions were facilitated by the Internet of Things (IoT) aimed at realizing smart buildings. Despite a general emphasis on sustainability, existing IoT-based solutions typically focus on monitoring and managing energy consumption and generation. Our interest in this article is to capture an expanded view of sustainability, including water and sanitation management, waste management and recycling monitoring, and the well-being and safety of building occupants or users. Specifically, we introduce an IoT architecture for monitoring and managing sustainability in smart buildings. To ensure relevance and applicability, we align the architecture elements with the criteria of the prominent certification called Leadership in Energy and Environmental Design. We further showcase deployment feasibility through available devices, as well as highlight outstanding challenges and opportunities.