The emerging paradigm of edge computing has proposed cloudlets to offload data and computations from mobile, resource-constrained devices. However, little attention has been paid to the question on where to deploy cloudlets in the context of smart city environments. In this vision paper, we propose to deploy cloudlets on a city-wide scale by leveraging three kinds of existing infrastructures: cellular base stations, routers and street lamps. We motivate the use of this infrastructure with real location data of nearly 50,000 access points from a major city. We provide an analysis on the potential coverage for the different cloudlet types. Besides spatial coverage, we also consider user traces from two mobile applications. Our results show that upgrading only a relatively small number of access points can lead to a city-scale cloudlet coverage. This is especially true for the coverage analysis of the mobility traces, where mobile users are within the communication range of a cloudlet-enabled access point most of the time.