Modeling user check-in behavior helps us gain useful insights about venues as well as the users visiting them. These insights are important in urban planning and recommender system applications. Since check-in behavior is the result of multiple factors, this paper focuses on studying two venue related factors, namely, area attraction and neighborhood competition. The former refers to the ability of a spatial area covering multiple venues to collectively attract check-ins from users, while the latter represents the extent to which a venue can compete with other venues in the same area for check-ins. We first embark on empirical studies to ascertain the two factors using three datasets gathered from users and venues of three major cities, Singapore, Jakarta and New York City. We then propose the visitation by area attractiveness and neighborhood competition (VAN) model incorporating area attraction and neighborhood competition factors. Our VAN model is also extended to incorporate social homophily so as to further enhance its modeling power. We evaluate VAN model using real world datasets against various state-of-the-art baselines. The results show that VAN model outperforms the baselines in check-in prediction task and its performance is robust under different parameter settings.