The term city infrastructures is often restricted to the physical elements of a city, while in practice it comprises both hard infrastructures for built environment and utilities, as well as soft infrastructures involving services, social groupings and personal skills. Part of the confusion is the lack of clarity about the role and delivery of city infrastructures and its relationship to livelihood and livability. To address this issue, a framework for soft and hard city infrastructures has been developed using results from two case studies to model the relationships, conflicts and connections between soft and hard infrastructures. The first case study concerns the abandonment of a planned urban regeneration project for the Italian City of Lucca in Tuscany where institutional inertia prevented regeneration of a derelict tobacco factory. The second case study concerned results from data analysis of contributions for a public consultation exercise for City of Christchurch in New Zealand. The syntactic data analytics using Flax software coupled with data visualisation demonstrated how an urban narrative can be constructed about citizen priorities based on a framework for soft and hard city infrastructures. The methodology enables citizen engagement through cultivating open processes of urban exploration that advocate ‘connected infrastructures’ thinking.