Public events, such as music concerts and fireworks displays, can cause irregular surges in cross-city travel demand, leading to potential overcrowding, travel delays, and public safety concerns. To better anticipate and accommodate such demand surges, it is essential to estimate cross-city visitor flows with awareness of public events. Although prior studies typically focused on the effects of a single mega event or disruptions around a single venue, this study introduces a generalizable framework to analyze visitor flows under diverse and concurrent events. We propose to leverage large language models (LLMs) to extract event features from multi-source online information and massive user-generated content on social media platforms. Specifically, social media popularity metrics are designed to capture the effects of online promotion and word-of-mouth in attracting visitors. An event-aware machine learning model is then adopted to uncover the specific impacts of different event features and ultimately predict visitor flows for upcoming events. Using Hong Kong as a case study, the framework is applied to predict daily flows of mainland Chinese visitors arriving at the city, achieving a testing R-squared of over 85%. We further investigate the heterogeneous event impacts on visitor numbers across different event types and major travel modes. Both promotional popularity and word-of-mouth popularity are found to be associated with increased visitor flows, but the specific effects vary by the event type. This association is more pronounced among visitors arriving by metro and high-speed rail, while it has less effect on air travelers. The findings can facilitate coordinated measures across government agencies and guide specialized transport policies, such as shuttle transit services to event venues, and comprehensive on-site traffic management strategies.