Tourism Recommender Systems (TRS) have traditionally focused on providing personalized travel suggestions, often prioritizing user preferences without considering broader sustainability goals. Integrating sustainability into TRS has become essential with the increasing need to balance environmental impact, local community interests, and visitor satisfaction. This paper proposes a novel approach to enhancing TRS for sustainable city trips using Large Language Models (LLMs) and a modified Retrieval-Augmented Generation (RAG) pipeline. We enhance the traditional RAG system by incorporating a sustainability metric based on a city's popularity and seasonal demand during the prompt augmentation phase. This modification, called Sustainability Augmented Reranking (SAR), ensures the system's recommendations align with sustainability goals. Evaluations using popular open-source LLMs, such as Llama-3.1-Instruct-8B and Mistral-Instruct-7B, demonstrate that the SAR-enhanced approach consistently matches or outperforms the baseline (without SAR) across most metrics, highlighting the benefits of incorporating sustainability into TRS.