Airports play a vital role in global travel, serving millions of passengers daily. With more people traveling by air, airport service quality improvement is more important than ever to ensure continued passenger satisfaction and effective airport operation. Traditional methods for assessing Airport Service Quality (ASQ), such as structured surveys and sentiment analysis, often fail to capture the full spectrum of passenger experiences. Existing studies rely on sentiment scoring and topic modelling, which provide broad insights but lack the depth to identify specific service issues. This research proposes a novel approach leveraging Large Language Models (LLMs) to automate the analysis of airport customer reviews. Our methodology involves a four-phase process: (1) identification of extreme positive and extreme negative reviews using clustering-based methods on the sentiment scores and customer ratings, (2) keyword extraction using LLMs, (3) keywords categorization and (4) topics generation. The proposed method is applied to the Skytrax airport reviews dataset. With the combination of LLM-based keyword extraction and topic modelling, our system gives a richer understanding of passengers' experience in the form of overt concerns such as security delays, unclean facilities, or unfriendly staff interaction. This study aims to help airports make better decisions and improve customer experiences. Our findings demonstrate that LLMs can significantly enhance the granularity and relevance of ASQ insights compared to traditional methods. The proposed framework presents a scalable, automated solution for airport operators to systematically improve passenger experience and operational efficiency based on unstructured feedback.