Cities are characterized by concentrating population, economic activity and services. However, not all cities are equal and a natural hierarchy at local, regional or global scales spontaneously emerges. In this work, we introduce a method to quantify city influence using geolocated tweets to characterize human mobility. Rome and Paris appear consistently as the cities attracting most diverse visitors. The ratio between locals and non-local visitors turns out to be fundamental for a city to truly be global. Focusing only on urban residents' mobility flows, a city-to-city network can be constructed. This network allows us to analyse centrality measures at different scales. New York and London play a central role on the global scale, while urban rankings suffer substantial changes if the focus is set at a regional level.