Urban green infrastructure can help cities tackle biodiversity loss and support well-being, but also contribute to climate change mitigation. This can be enhanced with green infrastructure policies that favor biodiversity, residential well-being, or climate benefits such as carbon sequestration. However, assessing public support for policies favoring specific green infrastructure outcomes, or potential trade-offs between them, is vital to understanding the social implications that such policies may have upon implementation. This paper presents the results of a public participation GIS (PPGIS) survey (n = 3 237) in Helsinki, Finland, concerning public support for policies favoring diverse climate, biodiversity, and well-being outcomes in green infrastructure. The results of the survey, derived with spatial and aspatial analyses, indicate that urban residents strongly support green infrastructure policies that favor climate benefits such as carbon sequestration, and are more willing to compromise the well-being benefits, rather than the biodiversity, of green infrastructure in favor of climate benefits. The results also reveal how support for policies favoring different green infrastructure outcomes varies spatially across the city, manifesting into priority areas of support for climate, biodiversity, and well-being outcomes. Finally, different ways of valuing and utilizing green infrastructure, and the socio-economic background of the respondents, predict support for policies favoring different green infrastructure outcomes. Our methods and results help take global political targets of mitigating climate change and reversing biodiversity loss into practice in cities in a manner that acknowledges the plurality of understandings on how green infrastructure should be managed, for whom, and most importantly, where.