Major interest is currently given to the integration of clusters of virtualization servers, also referred to as 'cloudlets' or 'edge clouds', into the access network to allow higher performance and reliability in the access to mobile edge computing services. We tackle the edge cloud network design problem for mobile access networks. The model is such that the virtual machines (VMs) are associated with mobile users and are allocated to cloudlets. Designing an edge cloud network implies first determining where to install cloudlet facilities among the available sites, then assigning sets of access points, such as base stations to cloudlets, while supporting VM orchestration and considering partial user mobility information, as well as the satisfaction of service-level agreements. We present link-path formulations supported by heuristics to compute solutions in reasonable time. We qualify the advantage in considering mobility for both users and VMs as up to 20% less users not satisfied in their SLA with a little increase of opened facilities. We compare two VM mobility modes, bulk and live migration, as a function of mobile cloud service requirements, determining that a high preference should be given to live migration, while bulk migrations seem to be a feasible alternative on delay-stringent tiny-disk services, such as augmented reality support, and only with further relaxation on network constraints.