The rapid adoption of large language models (LLMs) has led to significant energy consumption and carbon emissions, posing a critical challenge to the sustainability of generative AI technologies. This paper explores the integration of energy-efficient optimization techniques in the deployment of LLMs to address these environmental concerns. We present a case study and framework that demonstrate how strategic quantization and local inference techniques can substantially lower the carbon footprints of LLMs without compromising their operational effectiveness. Experimental results reveal that these methods can reduce energy consumption and carbon emissions by up to 45\% post quantization, making them particularly suitable for resource-constrained environments. The findings provide actionable insights for achieving sustainability in AI while maintaining high levels of accuracy and responsiveness.