This study examines how the Sustainable Development Goals (SDGs) can be leveraged to facilitate strategic change towards sustainability involving multiple stakeholders in a pluralistic city environment. By drawing on an exemplary case study of the localisation of the SDGs in Bristol, a medium-sized UK city, we show how the goals can operate as a boundary object. In particular, we identify a pattern in which the discursive localisation of the SDGs moved from problematisation and visioning through strategising and structuring towards embedding and performing. In addition, we elaborate on the three tensions that the SDGs help participants to understand and use productively, that is, across scale, time and different ways of valuing. Our study contributes to research on strategic change in pluralistic settings, such as cities, by offering a nuanced account of the discursive use of the SDGs by organisations involved in a city’s sustainable development. Furthermore, by proposing a framework based on the specific tensions that play an important role in the discursive localisation, our study advances research on the role of city strategising and practice more generally.