Pervasive broadband access will transform cities to the net social, environmental and economic benefit of the e-City dweller as did the introduction of utility and transport network infrastructures. Yet without action, the quantity of greenhouse gas emissions attributable to the increasing energy consumption of access networks will become a serious threat to the environment. This paper introduces the vision of a 'sustainable Digital City' and then considers strategies to overcome economic and technical hurdles faced by engineers responsible for developing the information and communications technology (ICT) network infrastructure of a Digital City. In particular, ICT energy consumption, already an issue from an operating cost perspective, is responsible for 3 % of global energy consumption and is growing unsustainably. A grand challenge is to conceive of networks, systems and devices that together can cap wireless network energy consumption whilst accommodating growth in the number of subscribers and the bandwidth of services. This paper provides some first research directions to tackle this grand challenge. A distributed antenna system with radio frequency (RF) transport over an optical fibre (or optical wireless in benign environments) distribution network is identified as best suited to wireless access in cluttered urban environments expected in a Digital City from an energy consumption perspective. This is a similar architecture to Radio-over-Fibre which, for decades, has been synonymous with RF transport over analogue intensity-modulated direct detection optical links. However, it is suggested herein that digital coherent optical transport of RF holds greater promise than the orthodox approach. The composition of the wireless and optical channels is then linear, which eases the digital signal processing tasks and permits robust wireless protocols to be used end-to-end natively which offers gains in terms of capacity and energy efficiency. The arguments are supported by simulation studies of distributed antenna systems and digital coherent Radio-over-Fibre links.