The expansion of short-term rental platforms, such as Airbnb, has significantly disrupted local housing markets, often leading to increased rental prices and housing affordability issues. Accurately forecasting regional Airbnb market trends can thus offer critical insights for policymakers and urban planners aiming to mitigate these impacts. This study proposes a novel time-series forecasting framework to predict three key Airbnb indicators -- Revenue, Reservation Days, and Number of Reservations -- at the regional level. Using a sliding-window approach, the model forecasts trends 1 to 3 months ahead. Unlike prior studies that focus on individual listings at fixed time points, our approach constructs regional representations by integrating listing features with external contextual factors such as urban accessibility and human mobility. We convert structured tabular data into prompt-based inputs for a Large Language Model (LLM), producing comprehensive regional embeddings. These embeddings are then fed into advanced time-series models (RNN, LSTM, Transformer) to better capture complex spatio-temporal dynamics. Experiments on Seoul's Airbnb dataset show that our method reduces both average RMSE and MAE by approximately 48% compared to conventional baselines, including traditional statistical and machine learning models. Our framework not only improves forecasting accuracy but also offers practical insights for detecting oversupplied regions and supporting data-driven urban policy decisions.