Among the many functions a smart city must support, transportation dominates in terms of resource consumption, strain on the environment, and frustration of its citizens. We study transportation networks under two different routing policies, the commonly assumed selfish user-centric routing policy and a socially optimal system-centric one. We consider a performance metric of efficiency-the Price of Anarchy (PoA)-defined as the ratio of the total travel latency cost under selfish routing over the corresponding quantity under socially optimal routing. We develop a data-driven approach to estimate the PoA, which we subsequently use to conduct a case study using extensive actual traffic data from the Eastern Massachusetts road network. To estimate the PoA, our approach learns from data a complete model of the transportation network, including origin-destination demand and user preferences. We leverage this model to propose possible strategies to reduce the PoA and increase efficiency.