Thanks to the various advantages over conventional cars, autonomous vehicles (AVs) will take a more important role in the future transportation system. Since AVs are typically electric vehicles (EVs), they can contribute to vehicle-to-grid (V2G) services. While it is generally not feasible to dictate EV routes, we can design AV travel plans to fulfill certain system-wide objectives. In this paper, we focus on the AVs looking for parking and study how they can be led to appropriate parking facilities to support V2G services. We formulate the problem as an integer linear program (ILP). It can be solved by a standard ILP solver but the required long computational time may not be acceptable in practical scenarios. To overcome this, we also develop a more efficient heuristic. We perform extensive simulations to study different perspectives on solving the problem. Simulation results reveal that the heuristic can significantly reduce the computational time with negligible degradation in objective function value. The quality of the optimal solution is insensitive to the number of available parking facilities. A coarser time scale can improve computational time but degrade the solution quality resulting in possible infeasible solution.