The Internet of Vehicles (IoV) vision encompasses a wide range of novel intelligent highway scenarios that rely on vehicles with an ever-increasing degree of autonomy and the prospect of sophisticated services like e-Horizon and cognitive driving assistance. The self-driving vehicle, on the other hand, entails a new passenger profile where sophisticated infotainment applications are expected to enhance the quality of travel. From the technical stand point, for this vision to become a reality a streamlined edge computing infrastructure, namely Vehicular Edge Computing (VEC), is required where computationally intensive workloads are offloaded to a nearby VEC infrastructure. However, the highly dynamic environment renders it difficult to efficiently operate a VEC system to yield the crisp performance required on an autonomous vehicle. In this setting, where to offload each task stands out as a crucial decision problem, and the conventional methods prove insufficient for its solution. In our work, we proposed a two-stage machine learning-based vehicular edge orchestrator which takes into account not only the task completion success but also the service time. To demonstrate how our approach performs in a realistic setting, we employed EdgeCloudSim to design extensive experiments where the characteristics of the vehicular applications, upload/download sizes, computational footprints of the tasks, the LAN, MAN and WAN network models, and the mobility are considered. Detailed performance evaluation of the proposed system via simulation is carried out where both overall and service type-specific performance scores in comparison with opponent schemes are reported.