Artificial intelligence (AI) has increasingly been integrated into various domains, significantly impacting geospatial applications. Machine learning (ML) and computer vision (CV) are critical in urban decision-making. However, urban AI implementation faces unique challenges. Academic literature on responsible AI largely focuses on general principles, with limited emphasis on the geospatial domain. This important gap in scholarly work could hinder effective AI integration in urban geospatial applications. Our study employs a multi-method approach, including a systematic academic literature review, word frequency analysis and insights from grey literature, to examine potential challenges and propose strategies for effective geospatial AI (GeoAI) integration. We identify a range of responsible practices relevant to the complexities of using AI in urban geospatial planning and its effective implementation. The review provides a comprehensive and actionable framework for responsible AI adoption in the geospatial domain, offering a roadmap for urban researchers and practitioners. It highlights ways to optimise AI benefits while minimising potential negative consequences, contributing to urban sustainability and equity.