Urban Nature-Based Solutions have emerged as sound strategies for urban climate change adaptation, but they lack effective decision-support tools. This paper proposes a decision-support framework that relies on Multi-Objective Optimization (MOO), the consideration of actual space availability, the consideration of the simultaneous objectives of climate change adaptation and water management, the integration of demand for cobenefits, and the participatory exploration of trade-offs for decision-makers. The MOO is applied to the case study of the French city of Bordeaux, to identify the optimal location of Groundwater Recharge Infrastructures (GRI) that include Nature-Based Solutions. It provides decision-makers with spatially explicit solutions for developing GRI, with the objectives of maximizing groundwater recharge, maximizing urban cooling, while minimizing opportunity costs, in the context of urban climate change adaptation. Results indicate an array of solutions between two polar strategies: large scale specialized grey solutions in most effective recharge areas, or diffused Nature-Based Solutions to satisfy citizen demand for multiple benefits. The participatory trade-off analysis proposed in this paper is a novel way to co-design spatial climate change adaptation strategies in urban contexts.