This paper studies the determinants of international students' mobility at the university level, focusing specifically on the role of tuition fees. We derive a gravity model from a Random Utility Maximization model of location choice for international students in the presence of capacity constraints of the hosting institutions. The last layer of the model is estimated using new data on student migration flows at the university level for Italy. We control for the potential endogeneity of tuition fees through a classical IV approach based on the status of the university. We obtain evidence for a clear and negative effect of fees on international student mobility and confirm the positive impact of the quality of the education. The estimations also support the important role of additional destination-specific variables such as host capacity, the expected return of education and the cost of living in the vicinity of the university.