Effective utility system management is fundamental and critical for ensuring the normal activities, operations, and services in cities and urban areas. In that regard, the advanced information and communication technologies underpinning smart cities enable close linkages and coordination of different sub-utility systems, which is now attracting research attention. To increase operational efficiency, we propose a two-stage optimal co-management model for an integrated urban utility system comprised of water, power, gas, and heating systems, namely integrated water-energy hubs (IWEHs). The proposed IWEH facilitates coordination between multi-energy and water sectors via close energy conversion, and can enhance the operational efficiency of an integrated urban utility system. In particular, we incorporate social-aware peer-to-peer (P2P) resource trading in the optimization model in which operators of an IWEH can trade energy and water with other interconnected IWEHs. To cope with renewable generation and load uncertainties and mitigate their negative impacts, a two-stage distributionally robust optimization is developed to capture the uncertainties, using a semidefinite programming reformulation. To demonstrate our model's effectiveness and practical values, we design representative case studies that simulate four interconnected IWEH communities. The results show that DRO is more effective than RO and SO for avoiding excessive conservativeness and rendering practical utilities, without requiring enormous data samples. This work reveals a desirable methodological approach to optimize the water-energy-social nexus for increased economic and system-usage efficiency for the entire (integrated) urban utility system. Furthermore, the proposed model incorporates social participations by citizens to engage in urban utility management for increased operation efficiency of cities and urban areas.