Artificial intelligence (AI) is increasingly embedded in how cities are governed, shaping decisions on mobility, land use, public services, and environmental management. Yet urban AI is predominantly governed through fragmented frameworks designed at national or corporate scales, offering limited guidance for municipal decision-making and overlooking place-specific social and ecological consequences. As the level of government closest to everyday urban life, cities are uniquely positioned to steer AI toward public value, but face persistent tensions between efficiency, equity, accountability, and sustainability. This paper argues that responsible urban AI cannot be governed through top-down or one-size-fits-all approaches. To address this, the study aims to conceptualise and advance a ground-up model of responsible urban AI governance that places cities and local governments at the centre of decision-making. It addresses the following research question: How can municipal authorities translate high-level ethical principles into practical, context-sensitive governance arrangements that respond to local capacities, risks, and public values? Drawing on global governance principles and illustrative city experiences, we propose a locally grounded, stage-based framework for municipal AI governance. The framework addresses institutional capacity gaps, fragmented responsibilities, and algorithmic externalities, advancing a participatory, place-sensitive, and adaptive model that aligns urban AI innovation with democratic legitimacy, social justice, and sustainable urban futures.