The increasing transition of human-robot interaction (HRI) context from controlled settings to dynamic, real-world public environments calls for enhanced adaptability in robotic systems. This can go beyond algorithmic navigation or traditional HRI strategies in structured settings, requiring the ability to navigate complex public urban systems containing multifaceted dynamics and various socio-technical needs. Therefore, our proposed workshop seeks to extend the boundaries of adaptive HRI research beyond predictable, semi-structured contexts and highlight opportunities for adaptable robot interactions in urban public environments. This half-day workshop aims to explore design opportunities and challenges in creating contextually-adaptive HRI within these spaces and establish a network of interested parties within the OzCHI research community. By fostering ongoing discussions, sharing of insights, and collaborations, we aim to catalyse future research that empowers robots to navigate the inherent uncertainties and complexities of real-world public interactions.