The electricity, heating, and transport sectors in urban areas all have to contribute to meeting stringent climate targets. Cities will face a transition from fossil fuels to renewable sources, with electricity acting as a cross-sectorial energy carrier. Consequently, the electricity demand of cities is expected to rise, in a situation that will be exacerbated by ongoing urbanisation and city growth. As the supply of electricity to cities is limited by transmission capacity from the national grid, city planning requires a detailed understanding of the options available for: decentralised electricity generation; synergies between the heating and electricity sectors; and flexibility through energy storage technologies. This work proposes an optimisation model that interconnects the electricity, heat, and transport sectors in cities. We analyse the investments in and operation of an urban energy system, using the City of Gothenburg as an example. We find that the availability of electricity from local solar PV together with thermal storage technologies increase the value of using power-to-heat technologies, such as heat pumps. High biomass prices together with strict climate targets enhance the importance of electricity in the district heating sector. At low biomass prices, CHP units fired by biomass are utilized over the whole model year. The model will be developed further in future studies, to include details on electric vehicle charging and other energy carriers.