This paper aims to provide an efficient solution for people in a city who drive their cars to visit several destinations, where they need to park for a while, but do not care about the visiting order. This instance of the multi-destination route planning problem is novel in terms of its constraints: the real-time traffic conditions and the real-time free parking conditions in the city. The paper proposes a novel Multi-Destination Vehicle Route Planning (MDVRP) system to optimize the travel time for all drivers. MDVRP's design has two components: a mobile app running on the drivers' smart phones that submits real-time route requests and guides the drivers toward destinations, and a server in the cloud that optimizes the routes by finding the most efficient order to visit the destinations. MDVRP uses TDTSP-FPA, an algorithm that finds the fastest route to the next destination and also assigns free curbside parking spaces that minimize the total travel time for drivers. We evaluate MDVRP using a driver trip dataset that contains real vehicular mobility traces of over two million drivers from the city of Cologne, Germany. By learning the spatio-temporal distribution of real driver destinations from this dataset, we build a novel experimental platform that simulates real, multi-destination driver trips. Extensive simulations executed over this platform demonstrate that TDTSP-FPA delivers the best performance when compared to three baseline algorithms.