The water system management problem has been widely investigated. However, the interdependencies between water and energy systems are significant and the effective co-optimization is required considering strong interconnections. This paper proposes a two-stage distributionally robust operation model for integrated water-energy nexus systems including power, gas and water systems networked with energy hub systems at a distribution level considering wind uncertainty. The presence of wind power uncertainty inevitably leads to risks in the optimization model. Accordingly, a coherent risk measure, i.e., conditional value-at-risk, is combined with the optimization objective to determine risk-averse operation schemes. This two-stage mean-risk distributionally robust optimization is solved by Bender's decomposition method. Both the day-ahead and real-time operation cost are minimized with an optimal set of scheduling the multi-energy infrastructures. Case studies focus on investigating the strong interdependencies among the four interconnected energy systems. Numerical results validate the economic effectiveness of IES through optimally coordinating the multi-energy infrastructures. The proposed model can provide system operators a powerful two-stage operation scheme to minimise operation cost under water-energy nexus considering risk caused by renewable uncertainties, thus benefiting customers with lower utility bills.