Determining when to leave for the airport is a complex problem shaped by flight delay risk, traffic, weather, airport congestion, and passenger-specific constraints. Existing services rely on isolated delay estimates or simple travel time calculations, failing to capture real-time context. We propose ORBIT, a decision-support system that generates personalized leave-by recommendations by integrating predictive models with real-time operational signals. The system combines user input normalization, real-time data acquisition, Transformer-based delay prediction, and LLM-based reasoning to jointly account for statistical forecasts and dynamic factors like congestion, previous-leg propagation, weather, traffic, and airport processing times. Instead of a standalone delay estimate, ORBIT produces an actionable and interpretable departure plan. We implement ORBIT as an interactive system and demonstrate its applicability. A video demo is available at https://youtu.be/fZX42jceIM4.