At the interface between airport airside and landside operations, the assignment of flights to gates is key to ensure efficient operations and a high quality of service for passengers. We propose a mixed-integer linear program for an integrated flight-to-gate assignment that considers both airside as well as landside constraints on the capabilities of facilities such as check-in, security or transfer to handle passengers. Moreover, our assignment is robust in that it constrains the probability of multiple flights being assigned to the same gate. Having obtained an integrated, robust flight-to-gate assignment, we analyse the associated quality of service at the landside facilities. Overall, our model supports the design of a robust, integrated airside-landside assignment of flights to gates at an airport.