We focus on the problem of optimal compute resource allocation and placement for the provision of a virtualized Content Delivery Network (CDN) service over a telecom operator's Network Functions Virtualization (NFV) infrastructure. Starting from a Quality of Experience (QoE)-driven decision on the necessary amount of CPU resources to allocate to satisfy a virtual CDN deployment request with QoE guarantees, we address the problem of distributing these resources to virtual machines and placing the latter to physical hosts, optimizing for the conflicting objectives of management cost and service availability, while respecting physical capacity, availability and cost constraints. We present a multi-objective optimization problem formulation, and provide efficient algorithms to solve it by relaxing some of the original problem's assumptions. Numerical results demonstrate how our solutions address the trade-off between service availability and cost, and show the benefits of our approach compared with resource placement algorithms which do not take this trade-off into account.